Search results for: impulsive differential equation

Authors: Sweta Sinha

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Rapid evolution of technology has changed language pedagogy as well as perspectives on language use, leading to strategic changes in discourse studies. We are now firmly embedded in a time when digital technologies have become an integral part of our daily lives. This has led to generalized approaches to English Language Teaching (ELT) which has raised two-pronged concerns in linguistically diverse settings: a) the diverse linguistic background of the learner might interfere/ intervene with the learning process and b) the differential level of already acquired knowledge of target language might make the classroom practices too easy or too difficult for the target group of learners. ELT needs a more systematic and differential pedagogical approach for greater efficiency and accuracy. The present research analyses the need of identifying learner groups based on different levels of target language proficiency based on a longitudinal study done on 150 undergraduate students. The learners were divided into five groups based on their performance on a twenty point scale in Listening Speaking Reading and Writing (LSRW). The groups were then subjected to varying durations of technology aided language learning sessions and their performance was recorded again on the same scale. Identifying groups and introducing differential teaching and learning strategies led to better results compared to generalized teaching strategies. Language teaching includes different aspects: the organizational, the technological, the sociological, the psychological, the pedagogical and the linguistic. And a facilitator must account for all these aspects in a carefully devised differential approach meeting the challenge of learner diversity. Apart from the justification of the formation of differential groups the paper attempts to devise framework to account for all these aspects in order to make ELT in multilingual setting much more effective.

Keywords: differential groups, English language teaching, language pedagogy, multilingualism, technology aided language learning

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Authors: Guesh Simretab Gebremedhin, Saumya Rajan Jena

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In this work, a septic B-spline scheme has been used to simplify the process of solving an approximate solution of the generalized Rosenau-regularized long-wave equation (GR-RLWE) with initial boundary conditions. The resulting system of first-order ODEs has dealt with Butcher’s fifth order Runge-Kutta (BFRK) approach without using finite difference techniques for discretizing the time-dependent variables at each time level. Here, no transformation or any kind of linearization technique is employed to tackle the nonlinearity of the equation. Two test problems have been selected for numerical justifications and comparisons with other researchers on the basis of efficiency, accuracy, and results of the two invariants Mᵢ (mass) and Eᵢ (energy) of some motion that has been used to test the conservative properties of the proposed scheme.

Keywords: septic B-spline scheme, Butcher's fifth order Runge-Kutta approach, error norms, generalized Rosenau-RLW equation

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Authors: A. Bentabet, A. Aydin, N. Fenineche

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In this work, we try to determine the best analytical approximation of differential cross sections, used generally in Monte Carlo simulation, to study the electron/positron slowing down in solid targets in the energy range up to 10 keV. Actually, our comparative study was carried out on the angular distribution of the scattering angle, the elastic total and the first transport cross sections which are the essential quantities used generally in the electron/positron transport study by using both stochastic and deterministic methods. Indeed, the obtained results using the relativistic partial wave expansion method and the backscattering coefficient experimental data are used as criteria to evaluate the used model.

Keywords: differential cross-section, backscattering coefficient, Rutherford cross-section, Vicanek and Urbassek theory

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Authors: Jian-Ping Yu, Wen-Xiu Ma, Yong-Li Sun, Chaudry Masood Khalique

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In this paper, a 2d Toda equation is studied, which is a classical integrable system and plays a vital role in mathematics, physics and other areas. New lump-type solution is constructed by using the Hirota bilinear method. One interesting feature of this research is that this lump-type solutions possesses two types of multiple-lump-type waves, which are one- and two-lump-type waves. Moreover, the corresponding 3d plots, density plots and contour plots are given to show the dynamical features of the obtained multiple-lump-type solutions.

Keywords: 2d Toda equation, Hirota bilinear method, Lump-type solution, multiple-lump-type solution

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Authors: Khashayar Kazemzadeh, Mohammad Hanif Dasoomi

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According to the increasing volume of traffic, lane changing plays a crucial role in traffic flow. Lane changing in traffic depends on several factors including road geometrical design, speed, drivers’ behavioral characteristics, etc. A great deal of research has been carried out regarding these fields. Despite of the other significant factors, the drivers’ behavioral characteristics of lane changing has been emphasized in this paper. This paper has predicted the effective equation based on personal characteristics of lane changing by regression models.

Keywords: effective equation, lane changing, drivers’ behavioral characteristics, regression models

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Authors: Carlos A. Vega-Posada, Jeisson Alejandro Higuita-Villa, Julio C. Saldarriaga-Molina

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This paper presents a simplified analytical approach to conduct elastic stability and second-order lateral stiffness analyses of beam-column elements (i.e., piles) with generalized end-boundary conditions embedded on a homogeneous or non-homogeneous Pasternak foundation. The solution is derived using the well-known Differential Transformation Method (DTM), and it consists simply of solving a system of two linear algebraic equations. Using other conventional approaches to solve the governing differential equation of the proposed element can be cumbersome and the solution challenging to implement, especially when the non-homogeneity of the soil is considered. The proposed formulation includes the effects of i) any rotational or lateral transverse spring at the ends of the pile, ii) any external transverse load acting along the pile, iii) soil non-homogeneity, and iv) the second-parameter of the elastic foundation (i.e., shear layer connecting the springs at the top). A parametric study is conducted to investigate the effects of different modulus of subgrade reactions, degrees of non-homogeneities, and intermediate end-boundary conditions on the pile response. The same set of equations can be used to conduct both elastic stability and static analyses. Comprehensive examples are presented to show the simplicity and practicability of the proposed method.

Keywords: elastic stability, second-order lateral stiffness, soil-non-homogeneity, pile analysis

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Authors: Sylvain Perrin, Thomas Saillour

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The Grande-Motte port and seafront development project on the French Mediterranean coastline entailed evaluating wave impact loads (pressures and forces) on the new beach seawall and comparing the resulting scour potential at the base of the existing and new seawall. A physical model was built at ARTELIA’s hydraulics laboratory in Grenoble (France) to provide insight into the evolution of scouring overtime at the front of the wall, quasi-static and impulsive wave force intensity and distribution on the wall, and water and sand overtopping discharges over the wall. The beach was constituted of fine sand and approximately 50 m wide above mean sea level (MSL). Seabed slopes were in the range of 0.5% offshore to 1.5% closer to the beach. A smooth concrete structure will replace the existing concrete seawall with an elevated curved crown wall. Prior the start of breaking (at -7 m MSL contour), storm-driven maximum spectral significant wave heights of 2.8 m and 3.2 m were estimated for the benchmark historical storm event dated of 1997 and the 50-year return period storms respectively, resulting in 1 m high waves at the beach. For the wave load assessment, a tensor scale measured wave forces and moments and five piezo / piezo-resistive pressure sensors were placed on the wall. Light-weight sediment physical model and pressure and force measurements were performed with scale 1:18. The polyvinyl chloride light-weight particles used to model the prototype silty sand had a density of approximately 1 400 kg/m3 and a median diameter (d50) of 0.3 mm. Quantitative assessments of the seabed evolution were made using a measuring rod and also a laser scan survey. Testing demonstrated the occurrence of numerous impulsive wave impacts on the reflector (22%), induced not by direct wave breaking but mostly by wave run-up slamming on the top curved part of the wall. Wave forces of up to 264 kilonewtons and impulsive pressure spikes of up to 127 kilonewtons were measured. Maximum scour of -0.9 m was measured for the new seawall versus -0.6 m for the existing seawall, which is imputable to increased wave reflection (coefficient was 25.7 - 30.4% vs 23.4 - 28.6%). This paper presents a methodology for the setup and operation of a physical model in order to assess the hydrodynamic and morphodynamic processes at a beach seawall during storms events. It discusses the pros and cons of such methodology versus others, notably regarding structures peculiarities and model effects.

Keywords: beach, impacts, scour, seawall, waves

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Authors: Raheela Akhtar, Zafar Iqbal Chaudhary, Yongqun Oliver He, Muhammad Younus, Aftab Ahmad Anjum

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Brucella abortus is an intracellular pathogen affecting macrophages. Macrophages release some components such as lysozymes (LZ), reactive oxygen species (ROS) and reactive nitrite intermediates (RNI) which are important tools against intracellular survival of Brucella. The antibrucella activity of bovine and murine macrophages was compared following stimulation with Brucella abortus lipopolysaccharides. Our results revealed that murine macrophages were ten times more potent to produce antibrucella components than bovine macrophages. The differential production of these components explained the differential Brucella killing ability of these species that was measured in terms of intramacrophagic survival of Brucella in murine and bovine macrophages.

Keywords: bovine macrophages, Brucella abortus, cell stimulation, cytokines, Murine macrophages

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Authors: A. R. Nezamabadi, M. Veiskarami

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This paper studies free vibration of simply supported functionally graded beams with piezoelectric layers based on the first order shear deformation theory. The Young's modulus of beam is assumed to be graded continuously across the beam thickness. The governing equation is established. Resulting equation is solved using the Euler's equation. The effects of the constituent volume fractions, the influences of applied voltage on the vibration frequency are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data.

Keywords: mechanical buckling, functionally graded beam, first order shear deformation theory, free vibration

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Authors: H. N. Cheung

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Self-compassion encourages one to accept oneself, reduce self-criticism and self-judgment, and see one’s shortcomings and setbacks in a balanced view. Adolescent self-compassion is a crucial protective factor against mental illness. It is, however, affected by gender. Given the scarcity of self-compassion scales for adolescents, the current study evaluates the Self-Compassion Scale for Youth (SCS-Y) in a large cross-cultural sample and investigates how the subscales of SCS-Y relate to the dimensions of depressive symptoms across gender. Through the internet-based Qualtrics, a total of 2881 teenagers aged 12 to 18 years were recruited from Hong Kong (HK), China, and the United Kingdom. A Multiple Indicator Multiple Cause (MIMIC) model was used to evaluate measurement invariance of the SCS-Y, and differential item functioning (DIF) was checked across gender. Upon the establishment of the best model, a multigroup structural equation model (SEM) was built between factors of SCS-Y and Multidimensional depression assessment scale (MDAS) which assesses four dimensions of depressive symptoms (emotional, cognitive, somatic and interpersonal). The SCS-Y was shown to have good reliability and validity. The MIMIC model produced a good model fit for a hypothetical six-factor model (CFI = 0.980; TLI = 0.974; RMSEA = 0.038) and no item was flagged for DIF across gender. A gender difference was observed between SCS-Y factors and depression dimensions. Conclusions: The SCS-Y exhibits good psychometric characteristics, including measurement invariance across gender. The study also highlights the gender difference between self-compassion factors and depression dimensions.

Keywords: self compassion, gender, depression, structural equation modelling, MIMIC model

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Authors: Chao-Qing Dai

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Two families of exact travelling solutions for the discrete sine-Gordon equation are constructed based on the variable-coefficient Jacobian elliptic function method and different transformations. When the modulus of Jacobian elliptic function solutions tends to 1, soliton solutions can be obtained. Some soliton solutions degenerate into the known solutions in literatures. Moreover, dynamical properties of exact solutions are investigated. Our analysis and results may have potential values for certain applications in modern nonlinear science and textile engineering.

Keywords: exact solutions, variable-coefficient Jacobian elliptic function method, discrete sine-Gordon equation, dynamical behaviors

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Authors: Alexander P. Smirnov, Sergey A. Matveev, Dmitry A. Zheltkov, Eugene E. Tyrtyshnikov

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We propose a new computational technique for multidimensional (multicomponent) Smoluchowski coagulation equation. Using low-rank approximations in Tensor Train format of both the solution and the coagulation kernel, we accelerate the classical finite-difference Runge-Kutta scheme keeping its level of accuracy. The complexity of the taken finite-difference scheme is reduced from O(N^2d) to O(d^2 N log N ), where N is the number of grid nodes and d is a dimensionality of the problem. The efficiency and the accuracy of the new method are demonstrated on concrete problem with known analytical solution.

Keywords: tensor train decomposition, multicomponent Smoluchowski equation, runge-kutta scheme, convolution

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Authors: Renjie Liu, Junshuai Xue, Jiajia Yao, Guanlin Wu, Zumao L, Xueyan Yang, Fang Liu, Zhuang Guo

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Here, we report the study of the performance of AlN/GaN bipolar resonance tunneling diodes (BRTDs) using numerical simulations. The I-V characteristics of BRTDs show double negative differential resistance regions, which exhibit similar peak current density and peak-to-valley current ratio (PVCR). Investigations show that the PVCR can approach 4.6 for the first and 5.75 for the second negative resistance region. The appearance of the two negative differential resistance regions is realized by changing the collector material of conventional GaN RTD to P-doped GaN. As the bias increases, holes in the P-region and electrons in the N-region undergo resonant tunneling, respectively, resulting in two negative resistance regions. The appearance of two negative resistance regions benefits from the high AlN barrier and the precise regulation of the potential well thickness. This result shows the promise of GaN BRTDs in the development of multi-valued logic circuits.

Keywords: GaN bipolar resonant tunneling diode, double negative differential resistance regions, peak to valley current ratio, multi-valued logic

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Authors: Aymen Rhouma, Khaled Hcheichi, Sami Hafsi

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The article presents an application of Fractional Model Predictive Control (FMPC) to a fractional order thermal system using Controlled Auto Regressive Integrated Moving Average (CARIMA) model obtained by discretization of a continuous fractional differential equation. Moreover, the output deviation approach is exploited to design the K -step ahead output predictor, and the corresponding control law is obtained by solving a quadratic cost function. Experiment results onto a thermal system are presented to emphasize the performances and the effectiveness of the proposed predictive controller.

Keywords: fractional model predictive control, fractional order systems, thermal system, predictive control

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Authors: Ramazan I. Kadiev, Arcady Ponosov

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Mathematical models of gene regulatory networks can in many cases be described by ordinary differential equations with switching nonlinearities, where the initial value problem is ill-posed. Several regularization methods are known in the case of deterministic networks, but the presence of stochastic noise leads to several technical difficulties. In the presentation, it is proposed to apply the methods of the stochastic singular perturbation theory going back to Yu. Kabanov and Yu. Pergamentshchikov. This approach is used to regularize the above ill-posed problem, which, e.g., makes it possible to design stable numerical schemes. Several examples are provided in the presentation, which support the efficiency of the suggested analysis. The method can also be of interest in other fields of biomathematics, where differential equations contain switchings, e.g., in neural field models.

Keywords: ill-posed problems, singular perturbation analysis, stochastic differential equations, switching nonlinearities

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Authors: Mourad Hrizi

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In this paper, we study the inverse problem of reconstructing an interior interface D appearing in the elliptic partial differential equation: Δu+χ(D)u=0 from the knowledge of the boundary measurements. This problem arises from a semiconductor transistor model. We propose a new shape reconstruction procedure that is based on the Kohn-Vogelius formulation and the topological sensitivity method. The inverse problem is formulated as a topology optimization one. A topological sensitivity analysis is derived from a function. The unknown subdomain D is reconstructed using a level-set curve of the topological gradient. Finally, we give several examples to show the viability of our proposed method.

Keywords: inverse problem, topological optimization, topological gradient, Kohn-Vogelius formulation

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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: R. B. Ogunrinde, C. C. Jibunoh

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In this paper, a spectral decomposition method is developed for the direct integration of stiff and nonstiff homogeneous linear (ODE) systems with linear, constant, or zero right hand sides (RHSs). The method does not require iteration but obtains solutions at any random points of t, by direct evaluation, in the interval of integration. All the numerical solutions obtained for the class of systems coincide with the exact theoretical solutions. In particular, solutions of homogeneous linear systems, i.e. with zero RHS, conform to the exact analytical solutions of the systems in terms of t.

Keywords: spectral decomposition, linear RHS, homogeneous linear systems, eigenvalues of the Jacobian

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Authors: Salisu Ibrahim

Abstract:

The paper studies the commutativity associated with fractional order linear time-varying systems (LTVSs), which is an important area of study in control systems engineering. In this paper, we explore the properties of these systems and their ability to commute. We proposed the necessary and sufficient condition for commutativity for fractional order LTVSs. Through a simulation and mathematical analysis, we demonstrate that these systems exhibit commutativity under certain conditions. Our findings have implications for the design and control of fractional order systems in practical applications, science, and engineering. An example is given to show the effectiveness of the proposed method which is been computed by Mathematica and validated by the use of MATLAB (Simulink).

Keywords: fractional differential equation, physical systems, equivalent circuit, analog control

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Authors: Hui-Yun Cao, Hai-Qing Zhou

Abstract:

The high precision measurements and experiments play more and more important roles in particle physics and atomic physics. To analyse the precise experimental data sets, the corresponding precise and reliable theoretical calculations are necessary. Until now, the form factors of elemental constituents such as pion and proton are still attractive issues in current Quantum Chromodynamics (QCD). In this work, the two-photon-exchange (TPE) effects in ep→enπ⁺ at small -t are discussed within a hadronic model. Under the pion dominance approximation and the limit mₑ→0, the TPE contribution to the amplitude can be described by a scalar function. We calculate TPE contributions to the amplitude, and the unpolarized differential cross section with the only elastic intermediate state is considered. The results show that the TPE corrections to the unpolarized differential cross section are about from -4% to -20% at Q²=1-1.6 GeV². After considering the TPE corrections to the experimental data sets of unpolarized differential cross section, we analyze the TPE corrections to the separated cross sections σ(L,T,LT,TT). We find that the TPE corrections (at Q²=1-1.6 GeV²) to σL are about from -10% to -30%, to σT are about 20%, and to σ(LT,TT) are much larger. By these analyses, we conclude that the TPE contributions in ep→enπ⁺ at small -t are important to extract the separated cross sections σ(L,T,LT,TT) and the electromagnetic form factor of π⁺ in the experimental analysis.

Keywords: differential cross section, form factor, hadronic, two-photon

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Authors: Salisu Ibrahim

Abstract:

The paper studies the commutativity associated with fractional order linear time-varying systems (LTVSs), which is an important area of study in control systems engineering. In this paper, we explore the properties of these systems and their ability to commute. We proposed the necessary and sufficient condition for commutativity for fractional order LTVSs. Through a simulation and mathematical analysis, we demonstrate that these systems exhibit commutativity under certain conditions. Our findings have implications for the design and control of fractional order systems in practical applications, science, and engineering. An example is given to show the effectiveness of the proposed method which is been computed by Mathematica and validated by the use of Matlab (Simulink).

Keywords: fractional differential equation, physical systems, equivalent circuit, and analog control

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Authors: P. Karimi, A. H. Khedmati Bazkiaei

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The main goal of this study is to test differential neural network as a controller of smart structure and is to enumerate its advantages and disadvantages in comparison with other controllers. In this study, the smart structure has been considered as a Euler Bernoulli cantilever beam and it has been tried that it be under control with the use of vibration neural network resulting from movement. Also, a linear observer has been considered as a reference controller and has been compared its results. The considered vibration charts and the controlled state have been recounted in the final part of this text. The obtained result show that neural observer has better performance in comparison to the implemented linear observer.

Keywords: smart material, on-line differential artificial neural network, active control, finite element method

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Authors: Teh Raihana Nazirah Roslan, Siti Zulaiha Ibrahim, Sharmila Karim

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A warrant is a financial contract that confers the right but not the obligation, to buy or sell a security at a certain price before expiration. The standard procedure to value equity warrants using call option pricing models such as the Black–Scholes model had been proven to contain many flaws, such as the assumption of constant interest rate and constant volatility. In fact, existing alternative models were found focusing more on demonstrating techniques for pricing, rather than empirical testing. Therefore, a mathematical model for pricing and analyzing equity warrants which comprises stochastic interest rate and stochastic volatility is essential to incorporate the dynamic relationships between the identified variables and illustrate the real market. Here, the aim is to develop dynamic pricing formulations for hybrid equity warrants by incorporating stochastic interest rates from the Cox-Ingersoll-Ross (CIR) model, along with stochastic volatility from the Heston model. The development of the model involves the derivations of stochastic differential equations that govern the model dynamics. The resulting equations which involve Cauchy problem and heat equations are then solved using partial differential equation approaches. The analytical pricing formulas obtained in this study comply with the form of analytical expressions embedded in the Black-Scholes model and other existing pricing models for equity warrants. This facilitates the practicality of this proposed formula for comparison purposes and further empirical study.

Keywords: Cox-Ingersoll-Ross model, equity warrants, Heston model, hybrid models, stochastic

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Authors: Raphael Zanella

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This works deals with the finite element approximation of axisymmetric problems. The weak formulation of the heat equation under the axisymmetry assumption is established for continuous finite elements. The weak formulation is implemented in a C++ solver with implicit march-in-time. The code is verified by space and time convergence tests using a manufactured solution. The solving of an example problem with an axisymmetric formulation is compared to that with a full-3D formulation. Both formulations lead to the same result, but the code based on the axisymmetric formulation is much faster due to the lower number of degrees of freedom. This confirms the correctness of our approach and the interest in using an axisymmetric formulation when it is possible.

Keywords: axisymmetric problem, continuous finite elements, heat equation, weak formulation

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Authors: J. J. Peña, J. Morales, J. García-Ravelo, L. Arcos-Díaz

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The Point canonical transformation method is applied for solving the Schrödinger equation with position-dependent mass. This class of problem has been solved for continuous mass distributions. In this work, a staggered mass distribution for the case of a free particle in an infinite square well potential has been proposed. The continuity conditions as well as normalization for the wave function are also considered. The proposal can be used for dealing with other kind of staggered mass distributions in the Schrödinger equation with different quantum potentials.

Keywords: free particle, point canonical transformation method, position-dependent mass, staggered mass distribution

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Authors: Nur Azzammudin Rahmat, Ismail Musirin, Ahmad Farid Abidin

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Economic load dispatch is performed by the utilities in order to determine the best generation level at the most feasible operating cost. In order to guarantee satisfying energy delivery to the consumer, a precise calculation of generation level is required. In order to achieve accurate and practical solution, several considerations such as prohibited operating zones, valve-point effect and ramp-rate limit need to be taken into account. However, these considerations cause the optimization to become complex and difficult to solve. This research focuses on the valve-point effect that causes ripple in the fuel-cost curve. This paper also proposes Differential Evolution Immunized Ant Colony Optimization (DEIANT) in solving economic load dispatch problem with valve-point effect. Comparative studies involving DEIANT, EP and ACO are conducted on IEEE 30-Bus RTS for performance assessments. Results indicate that DEIANT is superior to the other compared methods in terms of calculating lower operating cost and power loss.

Keywords: ant colony optimization (ACO), differential evolution (DE), differential evolution immunized ant colony optimization (DEIANT), economic load dispatch (ELD)

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Authors: Ya-Fen Lee, Yun-Yao Chi

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The study aims to explore the relationship between risk perceptions of rockfall and revisit intention using a Structural Equation Modelling (SEM) analysis. A total of 573 valid questionnaires are collected from travelers to Taroko National Park, Taiwan. The findings show the majority of travellers have the medium perception of rockfall risk, and are willing to revisit the Taroko National Park. The revisit intention to Taroko National Park is influenced by hazardous preferences, willingness-to-pay, obstruction and attraction. The risk perception has an indirect effect on revisit intention through influencing willingness-to-pay. The study results can be a reference for mitigation the rockfall disaster.

Keywords: risk perception, rockfall, revisit intention, structural equation modelling

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Authors: Carla E. O. de Moraes, Gladson O. Antunes, Mauro A. Rincon

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The aim of this paper is to study the internal stabilization of the Bernoulli-Euler equation numerically. For this, we consider a square plate subjected to a feedback/damping force distributed only in a subdomain. An algorithm for obtaining an approximate solution to this problem was proposed and implemented. The numerical method used was the Finite Difference Method. Numerical simulations were performed and showed the behavior of the solution, confirming the theoretical results that have already been proved in the literature. In addition, we studied the validation of the numerical scheme proposed, followed by an analysis of the numerical error; and we conducted a study on the decay of the energy associated.

Keywords: Bernoulli-Euler plate equation, numerical simulations, stability, energy decay, finite difference method

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Authors: Jorge Olivares, Fernando Maass, Pablo Martin

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Fractional derivatives have been considered recently as a way to solve different problems in Engineering. In this way, second kind modified Bessel functions are considered here. The order α fractional differential equations of second kind Bessel functions, Kᵥ(x), are studied with simple initial conditions. The Laplace transform and Caputo definition of fractional derivatives are considered. Solutions have been found for ν=1/3, 1/2, 2/3, -1/3, -1/2 and (-2/3). In these cases, the solutions are the sum of two hypergeometric functions. The α fractional derivatives have been for α=1/3, 1/2 and 2/3, and the above values of ν. No convergence has been found for the integer values of ν Furthermore when α has been considered as a rational found m/p, no general solution has been found. Clearly, this case is more difficult to treat than those of first kind Bessel Function.

Keywords: Caputo, modified Bessel functions, hypergeometric, linear fractional differential equations, transform Laplace

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Authors: Abhishek Jha, Manoj Kumar

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This paper proposes a new type of two wheels differential type odometry to estimate the next position and orientation of mobile robots. The proposed odometry is composed for two independent wheels with respective encoders. The two wheels rotate independently, and the change is determined by the difference in the velocity of the two wheels. Angular velocities of the two wheels are measured by rotary encoders. A mathematical model is proposed for the mobile robots to precisely move towards the goal. Using measured values of the two encoders, the current displacement vector of a mobile robot is calculated by kinematics of the mathematical model. Using the displacement vector, the next position and orientation of the mobile robot are estimated by proposed odometry. Result of simulator experiment by the developed odometry is shown.

Keywords: mobile robot, odometry, unicycle, differential type, encoders, infrared range sensors, kinematic model

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