Search results for: random differential inclusion

Authors: D. S. Palimkar

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The FRIGDI (functional random integrodifferential inclusion) seems to be new and includes several known random differential inclusions already studied in the literature as special cases have been discussed in the literature for various aspects of the solutions. In this paper, we prove the existence result for FIGDI under the non-convex case of multi-valued function involved in it.Using random fixed point theorem of B. C. Dhage and caratheodory condition. This result is new to the theory of differential inclusion.

Keywords: caratheodory condition, random differential inclusion, random solution, integro-differential inclusion

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Authors: Rajkumar N. Ingle

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In this paper, the existence of a solution of nonlinear functional random differential equations of the first order is proved under caratheodory condition. The study of the functional random differential equation has got importance in the random analysis of the dynamical systems of universal phenomena. Objectives: Nonlinear functional random differential equation is useful to the scientists, engineers, and mathematicians, who are engaged in N.F.R.D.E. analyzing a universal random phenomenon, govern by nonlinear random initial value problems of D.E. Applications of this in the theory of diffusion or heat conduction. Methodology: Using the concepts of probability theory, functional analysis, generally the existence theorems for the nonlinear F.R.D.E. are prove by using some tools such as fixed point theorem. The significance of the study: Our contribution will be the generalization of some well-known results in the theory of Nonlinear F.R.D.E.s. Further, it seems that our study will be useful to scientist, engineers, economists and mathematicians in their endeavors to analyses the nonlinear random problems of the universe in a better way.

Keywords: Random Fixed Point Theorem, functional random differential equation, N.F.R.D.E., universal random phenomenon

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Authors: Nini Johana Marín Rodríguez, William Fernando Oquendo Patino

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In this work, we model a coupled system where we explore the effects of steady and random behavior on a linear system like an extension of the classic Strogatz model. This is exemplified by modeling a couple love dynamics as a linear system of two coupled differential equations and studying its stability for four types of lovers chosen as CC='Cautious- Cautious', OO='Only other feelings', OP='Opposites' and RR='Romeo the Robot'. We explore the effects of, first, introducing saturation, and second, adding a random variation to one of the CC-type lover, which will shape his character by trying to model how its variability influences the dynamics between love and hate in couple in a long run relationship. This work could also be useful to model other kind of systems where interactions can be modeled as linear systems with external or internal random influence. We found the final results are not easy to predict and a strong dependence on initial conditions appear, which a signature of chaos.

Keywords: differential equations, dynamical systems, linear system, love dynamics

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Authors: Ayaz Ahmad

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In this work, we present the effect of noise on the solution of a partial differential equation (PDE) in three different setting. We shall first consider random initial condition for two nonlinear dispersive PDE the non linear Schrodinger equation and the Kortteweg –de vries equation and analyse their effect on some special solution , the soliton solutions.The second case considered a linear partial differential equation , the wave equation with random initial conditions allow to substantially decrease the computational and data storage costs of an algorithm to solve the inverse problem based on the boundary measurements of the solution of this equation. Finally, the third example considered is that of the linear transport equation with a singular drift term, when we shall show that the addition of a multiplicative noise term forbids the blow up of solutions under a very weak hypothesis for which we have finite time blow up of a solution in the deterministic case. Here we consider the problem of wave propagation, which is modelled by a nonlinear dispersive equation with noisy initial condition .As observed noise can also be introduced directly in the equations.

Keywords: drift term, finite time blow up, inverse problem, soliton solution

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Authors: P. W. Tsai, W. L. Hong, C. W. Chen, C. Y. Chen

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In this paper, we present a neural network (NN) based approach represent a nonlinear Tagagi-Sugeno (T-S) system. A linear differential inclusion (LDI) state-space representation is utilized to deal with the NN models. Taking advantage of the LDI representation, the stability conditions and controller design are derived for a class of nonlinear structural systems. Moreover, the concept of utilizing the Parallel Particle Swarm Optimization (PPSO) algorithm to solve the common P matrix under the stability criteria is given in this paper.

Keywords: Lyapunov stability, parallel particle swarm optimization, linear differential inclusion, artificial intelligence

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Authors: Christine Li, Amanda Robertson

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Epidermal inclusion cysts occur when epidermal cells are implanted in the dermis following trauma, or surgery. They are a rare cause of an umbilical mass, with very few cases previously reported following abdominal surgery. These lesions can present with a range of symptoms, including palpable mass, pain, redness, or discharge. This paper reports a case of an umbilical epidermal inclusion cyst in a 52-year-old female presenting with a six-week history of a painful, red umbilical lump on a background of two previous diagnostic laparoscopies. Abdominal computed tomography (CT) scans revealed non-specific soft tissue thickening in the umbilical region. This was successfully treated with complete excision of the lesion. Umbilical lumps are a common presentation but can represent a diagnostic challenge. The differential diagnosis should include an epidermal inclusion cyst, particularly in a patient who has had previous abdominal surgery, including laparoscopic surgery.

Keywords: epidermal inclusion cyst, laparoscopy, umbilical mass, umbilicus

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Authors: Ibtisam Masmali, Edwin Beggs

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In this paper, we take example of differential calculi, on the finite group A4. Then, we apply methods of non-commutative of non-commutative differential geometry to this example, and see how similar the results are to those of classical differential geometry.

Keywords: differential calculi, finite group A4, Christoffel symbols, covariant derivative, torsion compatible

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Authors: Y. N. Reddy

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The class of differential-difference equations which have characteristics of both classes, i.e., delay/advance and singularly perturbed behaviour is known as singularly perturbed differential-difference equations. The expression ‘positive shift’ and ‘negative shift’ are also used for ‘advance’ and ‘delay’ respectively. In general, an ordinary differential equation in which the highest order derivative is multiplied by a small positive parameter and containing at least one delay/advance is known as singularly perturbed differential-difference equation. Singularly perturbed differential-difference equations arise in the modelling of various practical phenomena in bioscience, engineering, control theory, specifically in variational problems, in describing the human pupil-light reflex, in a variety of models for physiological processes or diseases and first exit time problems in the modelling of the determination of expected time for the generation of action potential in nerve cells by random synaptic inputs in dendrites. In this paper, we envisage the use of Liouville Green Transformation to find the solution of singularly perturbed differential difference equations. First, using Taylor series, the given singularly perturbed differential difference equation is approximated by an asymptotically equivalent singularly perturbation problem. Then the Liouville Green Transformation is applied to get the solution. Several model examples are solved, and the results are compared with other methods. It is observed that the present method gives better approximate solutions.

Keywords: difference equations, differential equations, singular perturbations, boundary layer

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Authors: Tadesse Abera

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This study aimed to investigate the contribution of self-advocacy and engagement in the inclusion of SWDs in HEIs. A convergent parallel mixed methods design was employed. This article reports the quantitative strand. A total of 246 SWDs were selected through stratified proportionate random sampling technique from five public HEIs in Ethiopia. Data were collected through Self-advocacy questionnaire, student engagement scale, and college student experience questionnaire and analyzed through frequency, percentage, mean, standard deviation, correlation, one sample t-test and multiple regression. Both self-advocacy and engagement were found to have a predictive power on inclusion of respondents in the HEIs, where engagement was found to be more predictor. From the components of self-advocacy, knowledge of self and leadership and from engagement dimensions sense of belonging, cognitive, and valuing in their respective orders were found to have a stronger predictive power on the inclusion of respondents in the institutions. Based on the findings it was concluded that, if students with disabilities work hard to be self-determined, strive for realizing social justice, exert quality effort and seek active involvement, their inclusion in the institutions would be ensured.

Keywords: self-advocacy, engagement, inclusion, students with disabilities, higher education institution

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Authors: Ibrahim Baba

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The work examines the nature and causes of differential politics in Africa with particular reference to the sub-Saharan region of the continent. It also among other objectives provides alternative panacea to gender discrimination in African politics and offers solutions on how to promote political inclusion of all citizens in respect of gender differences in Africa. The work is conducted using library base documentation analysis.

Keywords: gender, political, participation, differential politics, sub-Saharan Africa

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Authors: Charlotte Brenner

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Teachers’ beleifs about inclusion are foundational to their implementation of inclusive teaching practices. Utilizing a longitudinal design and multiple case study methodology, this study investigates how teacher candidates’ instructional and practicum experiences shape their beliefs about inclusion in one teacher education program located in western Canada (N=20). Interview questions were developed through the lens of self-determinaiton theory and theory about teachers’ beleifs and inclusion. Preliminary thematic ananysis indicates that a 36-hour course focused on diversity and inclusion supports teacher candiates to deepen their understandings of: the need for inclusion in classrooms and strategies to promote inclusion. Furthermore, teacher candiates identified course components that fostered their developing understandings of inclusion. Future data will examine the stability of teacher candidates’ beliefs about inclusion and their implementation of inclusive teaching strategies throughout their practicum experiences.

Keywords: teacher candidates, inclusion, teacher education programs, beliefs

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Authors: Fuziyah Ishak, Siti Norazura Ahmad

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Volterra integro-differential equations appear in many models for real life phenomena. Since analytical solutions for this type of differential equations are hard and at times impossible to attain, engineers and scientists resort to numerical solutions that can be made as accurately as possible. Conventionally, numerical methods for ordinary differential equations are adapted to solve Volterra integro-differential equations. In this paper, numerical solution for solving Volterra integro-differential equation using extended trapezoidal method is described. Formulae for the integral and differential parts of the equation are presented. Numerical results show that the extended method is suitable for solving first order Volterra integro-differential equations.

Keywords: accuracy, extended trapezoidal method, numerical solution, Volterra integro-differential equations

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Authors: Godwin Chigozie Okpara, William Chimee Nwaoha

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The paper set out to stress on how financial inclusion index could be calculated and also investigated the impact of inclusive finance on inclusive growth in an emerging economy. In the light of these objectives, chi-wins method was used to calculate indexes of financial inclusion while co-integration and error correction model were used for evaluation of the impact of financial inclusion on inclusive growth. The result of the analysis revealed that financial inclusion while having a long-run relationship with GDP growth is an insignificant function of the growth of the economy. The speed of adjustment is correctly signed and significant. On the basis of these results, the researchers called for tireless efforts of government and banking sector in promoting financial inclusion in developing countries.

Keywords: chi-wins index, co-integration, error correction model, financial inclusion

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Authors: Melvin Ballera, Aldrich Olivar, Mary Soriano

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Digital computers nowadays must be able to have a utility that is capable of generating random numbers. Usually, computer-generated random numbers are not random given predefined values such as starting point and end points, making the sequence almost predictable. There are many applications of random numbers such business simulation, manufacturing, services domain, entertainment sector and other equally areas making worthwhile to design a unique method and to allow unpredictable random numbers. Applying stochastic simulation using linear congruential algorithm, it shows that as it increases the numbers of the seed and range the number randomly produced or selected by the computer becomes unique. If this implemented in an environment where random numbers are very much needed, the reliability of the random number is guaranteed.

Keywords: stochastic simulation, random numbers, linear congruential algorithm, pseudorandomness

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Authors: Francys Souza, Alberto Ohashi, Dorival Leao

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We present a general solution for finding the ε-optimal controls for non-Markovian stochastic systems as stochastic differential equations driven by Brownian motion, which is a problem recognized as a difficult solution. The contribution appears in the development of mathematical tools to deal with modeling and control of non-Markovian systems, whose applicability in different areas is well known. The methodology used consists to discretize the problem through a random discretization. In this way, we transform an infinite dimensional problem in a finite dimensional, thereafter we use measurable selection arguments, to find a control on an explicit form for the discretized problem. Then, we prove the control found for the discretized problem is a ε-optimal control for the original problem. Our theory provides a concrete description of a rather general class, among the principals, we can highlight financial problems such as portfolio control, hedging, super-hedging, pairs-trading and others. Therefore, our main contribution is the development of a tool to explicitly the ε-optimal control for non-Markovian stochastic systems. The pathwise analysis was made through a random discretization jointly with measurable selection arguments, has provided us with a structure to transform an infinite dimensional problem into a finite dimensional. The theory is applied to stochastic control problems based on path-dependent stochastic differential equations, where both drift and diffusion components are controlled. We are able to explicitly show optimal control with our method.

Keywords: dynamic programming equation, optimal control, stochastic control, stochastic differential equation

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Authors: M. Hamdi, R. Rhouma, S. Belghith

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Generating random numbers are mainly used to create secret keys or random sequences. It can be carried out by various techniques. In this paper we present a very simple and efficient pseudo-random number generator (PRNG) based on chaotic maps and S-Box tables. This technique adopted two main operations one to generate chaotic values using two logistic maps and the second to transform them into binary words using random S-Box tables. The simulation analysis indicates that our PRNG possessing excellent statistical and cryptographic properties.

Keywords: Random Numbers, Chaotic map, S-box, cryptography, statistical tests

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Authors: Kohei Inoue, Kenji Hara, Kiichi Urahama

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We describe a relationship between integral images and differential images. First, we derive a simple difference filter from conventional integral image. In the derivation, we show that an integral image and the corresponding differential image are related to each other by simultaneous linear equations, where the numbers of unknowns and equations are the same, and therefore, we can execute the integration and differentiation by solving the simultaneous equations. We applied the relationship to an image fusion problem, and experimentally verified the effectiveness of the proposed method.

Keywords: integral images, differential images, differential filters, image fusion

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Authors: Teoman Ozer, Ozlem Orhan

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This study deals with symmetry group properties and conservation laws of partial differential equations. We give a geometrical interpretation of notion of μ-prolongations of vector fields and of the related concept of μ-symmetry for partial differential equations. We show that these are in providing symmetry reduction of partial differential equations and systems and invariant solutions.

Keywords: λ-symmetry, μ-symmetry, classification, invariant solution

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Authors: Sumanta Kumar Saha, Jie Qin

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This study analyzes the impact of financial inclusion on gender inequality in 126 countries belonging to different income groups during the 2005–2019 period. Due to its positive influence on poverty alleviation, economic growth, women empowerment, and income inequality reduction, financial inclusion may help reduce gender equality. This study constructs a novel composite financial inclusion index and applies both fixed-effect panel estimation and instrumental variable approach to examine the impact of financial inclusion on gender inequality. The results indicate that financial inclusion can reduce gender inequality in developing and low- and lower-middle-income countries, but not in higher-income countries. The impact is not always immediate. Past financial inclusion initiatives have a significant influence on future gender inequality. Financial inclusion is also significant if the poverty level is high and women's access to financial services is low compared to men. When the poverty level is low, or women have equal access to financial services, financial inclusion does not significantly affect gender inequality. The study finds that compulsory education and improvement in institutional quality promote gender equality in developing countries apart from financial inclusion. The study proposes that lower-income countries use financial inclusion initiatives to improve gender equality. Other countries need to focus on other aspects such as promoting educational support and institutional quality improvements to achieve gender equality.

Keywords: financial inclusion, gender inequality, institutional quality, women empowerment

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Authors: Suha Alawadhi, Malak Alrasheed

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In the recent past, public participation in governments has been declined to a great extent, as citizens have been isolated from community life and their ability to articulate demands for good government has been noticeably decreased. However, the Internet has introduced new forms of interaction that could enhance different types of relationships, including government-public relationship. In fact, technology-enabled government has become a catalyst for enabling social inclusion. This exploratory study seeks to investigate public perceptions in Kuwait regarding the use of social media networks in government where social capital is built to achieve social inclusion. Social capital has been defined as social networks and connections amongst individuals, that are based on shared trust, ideas and norms, enable participants of a network to act effectively to pursue a shared objective. The quantitative method was used to generate empirical evidence. A questionnaire was designed to address the research objective and reflect the identified constructs: social capital dimensions (bridging, bonding and maintaining social capital), social inclusion, and social equality. In this pilot study, data was collected from a random sample of 61 subjects. The results indicate that all participants have a positive attitude towards the dimensions of social capital (bridging, bonding and maintaining), social inclusion and social equality constructs. Tests of identified constructs against demographic characteristics indicate that there are significant differences between male and female as they perceived bonding and maintaining social capital, social inclusion and social equality whereas no difference was identified in their perceptions of bridging social capital. Also, those who are aged 26-30 perceived bonding and maintaining social capital, social inclusion and social equality negatively compared to those aged 20-25, 31-35, and 40-above whose perceptions were positive. With regard to education, the results also show that those holding high school, university degree and diploma perceived maintaining social capital positively higher than with those who hold graduate degrees. Moreover, a regression model is proposed to study the effect of bridging, bonding, and maintaining social capital on social inclusion via social equality as a mediator. This exploratory study is necessary for testing the validity and reliability of the questionnaire which will be used in the main study that aims to investigate the perceptions of individuals towards building social capital to achieve social inclusion.

Keywords: government, social capital, social inclusion, social networks

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Authors: Kiran, Pooja Bhagat

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Inclusion of diversities is much talked and discussed for school education, mainly at the elementary level. However, not enough discourse has taken place as far as the promulgation of diversities from school education to higher education in terms of guarantee of access, retention and success of students belonging to the diverse groups is concerned. In view of this, the present paper attempts to look at the phenomenon of inclusion of diversities in higher education from the perspective of the people, who themselves are the part of the present system of higher education and aspiring to take up teaching at higher education level as profession. The paper focuses on exploring the awareness of the group under study about the inclusion of diversities at higher education, their perception of diversities, and the mechanism which they consider effective to facilitate inclusion.

Keywords: inclusion, higher education, perception, belief, attitude

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Authors: Yildiray Keskin, Omer Acan, Murat Akkus

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In this paper, the solution of fractional diffusion equations is presented by means of the reduced differential transform method. Fractional partial differential equations have special importance in engineering and sciences. Application of reduced differential transform method to this problem shows the rapid convergence of the sequence constructed by this method to the exact solution. The numerical results show that the approach is easy to implement and accurate when applied to fractional diffusion equations. The method introduces a promising tool for solving many fractional partial differential equations.

Keywords: fractional diffusion equations, Caputo fractional derivative, reduced differential transform method, partial

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Authors: Davies Obaromi, Qin Yongsong, James Ndege, Azeez Adeboye, Akinwumi Odeyemi

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The basic model usually used in disease mapping, is the Besag, York and Mollie (BYM) model and which combines the spatially structured and spatially unstructured priors as random effects. Bayesian Conditional Autoregressive (CAR) model is a disease mapping method that is commonly used for smoothening the relative risk of any disease as used in the Besag, York and Mollie (BYM) model. This model (CAR), which is also usually assigned as a prior to one of the spatial random effects in the BYM model, successfully uses information from adjacent sites to improve estimates for individual sites. To our knowledge, there are some unrealistic or counter-intuitive consequences on the posterior covariance matrix of the CAR prior for the spatial random effects. In the conventional BYM (Besag, York and Mollie) model, the spatially structured and the unstructured random components cannot be seen independently, and which challenges the prior definitions for the hyperparameters of the two random effects. Therefore, the main objective of this study is to construct and utilize an extended Bayesian spatial CAR model for studying tuberculosis patterns in the Eastern Cape Province of South Africa, and then compare for flexibility with some existing CAR models. The results of the study revealed the flexibility and robustness of this alternative extended CAR to the commonly used CAR models by comparison, using the deviance information criteria. The extended Bayesian spatial CAR model is proved to be a useful and robust tool for disease modeling and as a prior for the structured spatial random effects because of the inclusion of an extra hyperparameter.

Keywords: Besag2, CAR models, disease mapping, INLA, spatial models

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Authors: Kamaljit Pati, Manas Kumar Mohanty, Sanjib Sadhu

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A heuristic has been designed to generate a random simple monotone polygon from a given set of ‘n’ points lying on a 2-Dimensional plane. Our heuristic generates a random monotone polygon in O(n) time after O(nℓogn) preprocessing time which is improved over the previous work where a random monotone polygon is produced in the same O(n) time but the preprocessing time is O(k) for n < k < n2. However, our heuristic does not generate all possible random polygons with uniform probability. The space complexity of our proposed heuristic is O(n).

Keywords: sorting, monotone polygon, visibility, chain

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Authors: F. Maass, P. Martin, J. Olivares

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The aim of this work is the application of the program GeoGebra in teaching the study of nonhomogeneous linear second order differential equations with constant coefficients. Different kind of functions or forces will be considered in the right hand side of the differential equations, in particular, the emphasis will be placed in the case of trigonometrical functions producing the resonance phenomena. In order to obtain this, the frequencies of the trigonometrical functions will be changed. Once the resonances appear, these have to be correlationated with the roots of the second order algebraic equation determined by the coefficients of the differential equation. In this way, the physics and engineering students will understand resonance effects and its consequences in the simplest way. A large variety of examples will be shown, using different kind of functions for the nonhomogeneous part of the differential equations.

Keywords: education, geogebra, ordinary differential equations, resonance

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Authors: Ali Dalirbod, Peyman Ahmadian

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Inclusions are unavoidable part of all steels. Non-metallic inclusions have significant effects on mechanical properties of steel. The effects of inclusion on stress concentration around the matrix/inclusion have been extensively studied. The results relating to single inclusion behavior, describe properly the behavior of stress but not the elongation drop. The raised stress in inclusion/matrix results in crack initiation. The influence of binary inclusions on stress concentration around matrix is a major aim of this work which is representative of the simple pattern distribution of non-metallic inclusions. Stress concentration around inclusions in this case depends on parameters like distance between two inclusions (d), angle between centrally linking line of two inclusions, load axis (φ), and rotational angle of inclusion (θ). FEM analysis was applied to investigate the highest and lowest ductility versus varying parameters above. The simulation results show that there is a critical distance between two cubic inclusions in which bigger than the threshold, the stress, and strain field in matrix/inclusions interface converts into individual fields around each inclusion.

Keywords: nitride inclusion, simulation, tensile properties, inclusion-matrix interface

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Authors: Mesfin Abebe Molla

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This research aims to examine the practices of inclusion of the hard of hearing and deaf students in regular schools. It also focuses on exploring strategies for optimal benefits of students with Hard of Hearing and Deaf (HH-D) from inclusion. Concurrent mixed methods research design was used to collect quantitative and qualitative data. The instruments used to gather data for this study were questionnaire, semi- structured interview, and observations. A total of 102 HH-D students and 42 primary and High School teachers were selected using simple random sampling technique and used as participants to collect quantitative data. Non-probability sampling technique was also employed to select 14 participants (4-school principals, 6-teachers and 4-parents of HH-D students) and they were interviewed to collect qualitative data. Descriptive and inferential statistical techniques (independent sample t-test, one way ANOVA and Multiple regressions) were employed to analyze quantitative data. Qualitative data were also analyzed qualitatively by theme analysis. The findings reported that there were individual principals’, teachers’ and parents’ strong commitment and efforts for practicing inclusion of HH-D students effectively; however, most of the core values of inclusion were missing in both schools. Most of the teachers (78.6 %) and HH-D students (75.5%) had negative attitude and considerable reservations about the feasibility of inclusion of HH-D students in both schools. Furthermore, there was a statistically significant difference of attitude toward to inclusion between the two school’s teachers and the teachers’ who had taken and had not taken additional training on IE and sign language. The study also indicated that there was a statistically significant difference of attitude toward to inclusion between hard of hearing and deaf students. However, the overall contribution of the demographic variables of teachers and HH-D students on their attitude toward inclusion is not statistically significant. The finding also showed that HH-D students did not have access to modified curriculum which would maximize their abilities and help them to learn together with their hearing peers. In addition, there is no clear and adequate direction for the medium of instruction. Poor school organization and management, lack of commitment, financial resources, collaboration and teachers’ inadequate training on Inclusive Education (IE) and sign language, large class size, inappropriate assessment procedure, lack of trained deaf adult personnel who can serve as role model for HH-D students and lack of parents and community members’ involvement were some of the major factors that affect the practicing inclusion of students HH-D. Finally, recommendations are made to improve the practices of inclusion of HH-D students and to make inclusion of HH-D students an integrated part of Ethiopian education based on the findings of the study.

Keywords: deaf, hard of hearing, inclusion, regular schools

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Authors: Yaping Zhao

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In the present study, the exact solutions for the steady response of quasi-linear systems under non-white wide-band random excitation are considered by means of the stochastic averaging method. The non linearity of the systems contains the power-law damping and the cross-product term of the power-law damping and displacement. The drift and diffusion coefficients of the Fokker-Planck-Kolmogorov (FPK) equation after averaging are obtained by a succinct approach. After solving the averaged FPK equation, the joint probability density function and the marginal probability density function in steady state are attained. In the process of resolving, the eigenvalue problem of ordinary differential equation is handled by integral equation method. Some new results are acquired and the novel method to deal with the problems in nonlinear random vibration is proposed.

Keywords: random vibration, stochastic averaging method, FPK equation, transition probability density

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Authors: Shama Urooj

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The present work investigates the relationship among financial inclusion, modernization, and energy performance in SCO member countries during the years 2011–2021. PCA is used to create composite indexes of financial inclusion, modernization, and energy performance. We used panel regression models that are both reliable and heteroscedasticity-consistent to look at the relationship among variables. The findings indicate that financial inclusion (FI) and modernization, along with the increased FDI, all appear to contribute to the energy performance in the SCO member countries. However, per capita GDP has a negative impact on energy performance. These results are unbiased and consistent with the robust results obtained by applying different econometric models. Feasible Generalized Least Square (FGLS) estimation is also used for checking the uniformity of the main model results. This research work concludes that there has been no policy coherence in SCO member countries regarding the coordination of growing financial inclusion and modernization for energy sustainability in recent years. In order to improve energy performance with modern development, policies regarding financial inclusion and modernization need be integrated both at national as well as international levels.

Keywords: financial inclusion, energy performance, modernization, technological development, SCO.

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Authors: Lev Idels, Arcady Ponosov

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Stochastic fractional differential equations have recently attracted considerable attention, as they have been used to model real-world processes, which are subject to natural memory effects and measurement uncertainties. Compared to conventional hereditary differential equations, one of the advantages of fractional differential equations is related to more realistic geometric properties of their trajectories that do not intersect in the phase space. In this report, a Peano-like existence theorem for nonlinear stochastic fractional differential equations is proven under very general hypotheses. Several specific classes of equations are checked to satisfy these hypotheses, including delay equations driven by the fractional Brownian motion, stochastic fractional neutral equations and many others.

Keywords: delay equations, operator methods, stochastic noise, weak solutions

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