Search results for: first derivative

Authors: Bangkit Adhi Nugraha, Bambang Suripto

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On September 2016 Bank Indonesia (BI) release regulation no.18/18/PBI/2016 that permit bank clients for using the FX option call spread USD/IDR. Basically, this product is a combination between clients buy FX call option (pay premium) and sell FX call option (receive premium) to protect against currency depreciation while also capping the potential upside with cheap premium cost. BI classifies this product as a structured product. The structured product is combination at least two financial instruments, either derivative or non-derivative instruments. The call spread is the first structured product against IDR permitted by BI since 2009 as response the demand increase from Indonesia firms on FX hedging through derivative for protecting market risk their foreign currency asset or liability. The composition of hedging products on Indonesian FX market increase from 35% on 2015 to 40% on 2016, the majority on swap product (FX forward, FX swap, cross currency swap). Swap is formulated by interest rate difference of the two currency pairs. The cost of swap product is 7% for USD/IDR with one year USD/IDR volatility 13%. That cost level makes swap products seem expensive for hedging buyers. Because call spread cost (around 1.5-3%) cheaper than swap, the most Indonesian firms are using NDF FX call spread USD/IDR on offshore with outstanding amount around 10 billion USD. The cheaper cost of call spread is the main advantage for hedging buyers. The problem arises because BI regulation requires the call spread buyer doing the dynamic hedging. That means, if call spread buyer choose strike price 1 and strike price 2 and volatility USD/IDR exchange rate surpass strike price 2, then the call spread buyer must buy another call spread with strike price 1’ (strike price 1’ = strike price 2) and strike price 2’ (strike price 2’ > strike price 1‘). It could make the premium cost of call spread doubled or even more and dismiss the purpose of hedging buyer to find the cheapest hedging cost. It is very crucial for the buyer to choose best optimum strike price before entering into the transaction. To help hedging buyer find the optimum strike price and avoid expensive multiple premium cost, we observe ten years 2005-2015 historical data of USD/IDR volatility to be compared with the price movement of the call spread USD/IDR using Garman–Kohlhagen Model (as a common formula on FX option pricing). We use statistical tools to analysis data correlation, understand nature of call spread price movement over ten years, and determine factors affecting price movement. We select some range of strike price and tenor and calculate the probability of dynamic hedging to occur and how much it’s cost. We found USD/IDR currency pairs is too uncertain and make dynamic hedging riskier and more expensive. We validated this result using one year data and shown small RMS. The study result could be used to understand nature of FX call spread and determine optimum strike price for hedging plan.

Keywords: FX call spread USD/IDR, USD/IDR volatility statistical analysis, Garman–Kohlhagen Model on FX Option USD/IDR, Bank Indonesia Regulation no.18/18/PBI/2016

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Authors: İbrahim Aktaş, Árpád Baricz

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In this paper, the radii of star likeness of the Jackson and Hahn-Exton q-Bessel functions are considered, and for each of them three different normalizations is applied. By applying Euler-Rayleigh inequalities for the first positive zeros of these functions tight lower, and upper bounds for the radii of starlikeness of these functions are obtained. The Laguerre-Pólya class of real entire functions plays an important role in this study. In particular, we obtain some new bounds for the first positive zero of the derivative of the classical Bessel function of the first kind.

Keywords: bessel function, lommel function, radius of starlikeness and convexity, Struve function

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Authors: Dewi Retno Sari Saputro, Purnami Widyaningsih, Hendrika Handayani

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Extreme data on an observation can occur due to unusual circumstances in the observation. The data can provide important information that can’t be provided by other data so that its existence needs to be further investigated. The method for obtaining extreme data is one of them using maxima block method. The distribution of extreme data sets taken with the maxima block method is called the distribution of extreme values. Distribution of extreme values is Gumbel distribution with two parameters. The parameter estimation of Gumbel distribution with maximum likelihood method (ML) is difficult to determine its exact value so that it is necessary to solve the approach. The purpose of this study was to determine the parameter estimation of Gumbel distribution with quasi-Newton BFGS method. The quasi-Newton BFGS method is a numerical method used for nonlinear function optimization without constraint so that the method can be used for parameter estimation from Gumbel distribution whose distribution function is in the form of exponential doubel function. The quasi-New BFGS method is a development of the Newton method. The Newton method uses the second derivative to calculate the parameter value changes on each iteration. Newton's method is then modified with the addition of a step length to provide a guarantee of convergence when the second derivative requires complex calculations. In the quasi-Newton BFGS method, Newton's method is modified by updating both derivatives on each iteration. The parameter estimation of the Gumbel distribution by a numerical approach using the quasi-Newton BFGS method is done by calculating the parameter values that make the distribution function maximum. In this method, we need gradient vector and hessian matrix. This research is a theory research and application by studying several journals and textbooks. The results of this study obtained the quasi-Newton BFGS algorithm and estimation of Gumbel distribution parameters. The estimation method is then applied to daily rainfall data in Purworejo District to estimate the distribution parameters. This indicates that the high rainfall that occurred in Purworejo District decreased its intensity and the range of rainfall that occurred decreased.

Keywords: parameter estimation, Gumbel distribution, maximum likelihood, broyden fletcher goldfarb shanno (BFGS)quasi newton

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Authors: Nurudeen Ayeni, Kasali Bello, Ovi Abayeh

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Study of the effect of dye–resin complexation on the degree of dye absorption were carried out using Procion Blue MX-R to dye cotton fabric in the presence hexamethylol melamine (MR 6) and its phosphate derivative (MPR 4) for resination. The highest degree of dye exhaustion was obtained at 400 C for 1 hour with the resinated fabric showing more affinity for the dye than the ordinary fiber. Improved fastness properties was recorded which show a relatively higher stability of dye–resin–cellulose network formed.

Keywords: cotton fabric, reactive dye, dyeing, resination

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Authors: M. Ibrir, S. Berri, S. Lakel, D. Maouche And Y. Medkour

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We have performed first-principle calculations of the structural, electronic and magnetic properties of KFeF3, KCoF3, KMnF3, KVF3, using full-potential linearized augmented plane-wave (FP-LAPW) scheme within GGA. Features such as the lattice constant, bulk modulus and its pressure derivative are reported. Also, we have presented our results of the band structure and the density of states. The magnetic moments of KFeF3, KCoF3, KMnF3, KVF3 compounds are in most came from the exchange-splitting of X-3d orbital.

Keywords: Ab initio calculations, electronic structure, magnetic materials

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Authors: Nurudeen Afolami Ayeni, Kasali Adewale Bello

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Study of the effect of dye-resin complexation on the degree of dye absorption were carried out using Procion Blue MX-R to dye cotton fabric in the presence hexamethylol melamine (MR6) and its phosphate derivative (MPR4) for resination. The highest degree of dye exhaustion was obtained at 400C for 1 hour with the resinated fabric showing more affinity for the dye than the ordinary fibre. Improved fastness properties was recorded which show a relatively higher stability of dye-resin complex formed in the fibre.

Keywords: affinity, cotton, dyeing, reactive dye, resination

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Authors: Mei-Ling Chan, Jin-Ming Wu, Konstantin V. Kudryavtsev, Jih-Hwa Guh

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Prostate cancer is one of the most common malignant disease in men. KUD983 is an enantiomerically pure β-dipeptide derivative, which may have anti-cancer effects. In the present study, KUD983 exhibits powerful activity against hormone-refractory prostate cancer (HRPC) PC-3 and DU145 cells. The IC50 values of KUD983 in PC-3 and DU145 cells are 0.56±0.07M and 0.50±0.04 M respectively. KUD983 induced G1 arrest of the cell cycle and subsequent apoptosis associated with the down-regulation of several related proteins including cyclin D1, cyclin E and Cdk4, and the de-phosphorylation of RB. The protein expressions of nuclear and total c-Myc protein, which was able to regulate the expression of both cyclin D1 and cyclin E, were significantly suppressed by KUD983. Phosphoinositide 3-kinase (PI3K)/Akt/mammalian target of rapamycin (mTOR) is an important signaling pathway that influences the energy metabolism, cell cycle, proliferation, survival and apoptosis of cells, and is associated with numerous other signaling pathways. The Western Blot data revealed that KUD983 inhibited PI3K/Akt and mTOR/p70S6K/4E-BP1 pathways. The transient transfection of constitutively active myristylated Akt (myr-Akt) cDNA significantly reversed KUD983-induced caspase activation but did not abolish the suppression of mTOR/p70S6K/4E-BP1 signaling cascade indicating the presence of both Akt-dependent and -independent pathways. Moreover, KUD983-induced effect was collaborated with the down-regulation of anti-apoptotic Bcl-2 members (e.g., Bcl-2, and Mcl-1) and IAP family members (e.g., survivin). Furthermore, KUD983 induced autophagic cell death using confocal microscopic examination, investigating the level of conversion of LC3-I to LC3-II and flow cytometric detection of AVO-positive cells. Taken together, the data suggest that KUD983 is an anticancer β-dipeptide against HRPCs through the inhibition of cell proliferation and induction of apoptotic and autophagic cell death. The suppression of signaling pathways mediated by c-Myc, PI3K/Akt and mTOR/p70S6K/4E-BP1 and the collaboration with down-regulation of Mcl-1 and survivin may indicate the mechanism of KUD983 against HRPC.

Keywords: β-dipeptide, hormone-refractory prostate cancer, mTOR, PI3K/Akt

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Authors: Hamza Rekab Djabri, Salah Daoud

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The present paper deals with the computational of structural and electronic properties of ThC and ThN compounds using density functional theory within generalized-gradient (GGA) apraximation and local density approximation (LDA). We employ the full potential linear muffin-tin orbitals (FP-LMTO) as implemented in the Lmtart code. We have used to examine structure parameter in eight different structures such as in NaCl (B1), CsCl (B2), ZB (B3), NiAs (B8), PbO (B10), Wurtzite (B4) , HCP (A3) βSn (A5) structures . The equilibrium lattice parameter, bulk modulus, and its pressure derivative were presented for all calculated phases. The calculated ground state properties are in good agreement with available experimental and theoretical results.

Keywords: DFT, GGA, LDA, properties structurales, ThC, ThN

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Authors: S. B. Provost, Hossein Zareamoghaddam

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A univariate density approximation technique whereby the derivative of the logarithm of a density function is assumed to be expressible as a rational function is introduced. This approach which extends Pearson’s curve system is solely based on the moments of a distribution up to a determinable order. Upon solving a system of linear equations, the coefficients of the polynomial ratio can readily be identified. An explicit solution to the integral representation of the resulting density approximant is then obtained. It will be explained that when utilised in conjunction with sample moments, this methodology lends itself to the modelling of ‘big data’. Applications to sets of univariate and bivariate observations will be presented.

Keywords: density estimation, log-density, moments, Pearson's curve system

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Authors: Johnson Oladele Fatokun, I. P. Akpan

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In this paper, the one-dimensional time dependent Schrödinger equation is discretized by the method of lines using a second order finite difference approximation to replace the second order spatial derivative. The evolving system of stiff ordinary differential equation (ODE) in time is solved numerically by an L-stable trapezoidal-like integrator. Results show accuracy of relative maximum error of order 10-4 in the interval of consideration. The performance of the method as compared to an existing scheme is considered favorable.

Keywords: Schrodinger’s equation, partial differential equations, method of lines (MOL), stiff ODE, trapezoidal-like integrator

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Authors: C. S. Bianca Sabrina, N. Egidio Raimundo, L. Alexandre Baratella, C. H. João Paulo

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This paper aims to present a study, with the theoretical concepts and applications of the Quadcopter, using the MATLAB simulator. In order to use this tool, the study of the stability of the drone through a Proportional - Integral - Derivative (PID) controller will be presented. After the stability study, some tests are done on the simulator and its results will be presented. From the mathematical model, it is possible to find the Newton-Euler angles, so that it is possible to stabilize the quadcopter in a certain position in the air, starting from the ground. In order to understand the impact of the controllers gain values on the stabilization of the Euler-Newton angles, three conditions will be tested with different controller gain values.

Keywords: controllers, drones, quadcopter, stability

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Authors: Parshanth Maroju, Ramandeep Behl, Sandile S. Motsa

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In this study, we proposed a simple and interesting family of fourth-order multi-point methods without memory for obtaining simple roots. This family requires only three functional evaluations (viz. two of functions f(xn), f(yn) and third one of its first-order derivative f'(xn)) per iteration. Moreover, the accuracy and validity of new schemes is tested by a number of numerical examples are also proposed to illustrate their accuracy by comparing them with the new existing optimal fourth-order methods available in the literature. It is found that they are very useful in high precision computations. Further, the dynamic study of these methods also supports the theoretical aspect.

Keywords: basins of attraction, nonlinear equations, simple roots, Newton's method

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Authors: Geetanjali Panda, Suvrakanti Chakraborty

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In this paper, Newton-like descent methods are proposed for unconstrained optimization problems, which use q-derivatives of the gradient of an objective function. First, a local scheme is developed with alternative sufficient optimality condition, and then the method is extended to a global scheme. Moreover, a variant of practical Newton scheme is also developed introducing a real sequence. Global convergence of these schemes is proved under some mild conditions. Numerical experiments and graphical illustrations are provided. Finally, the performance profiles on a test set show that the proposed schemes are competitive to the existing first-order schemes for optimization problems.

Keywords: Descent algorithm, line search method, q calculus, Quasi Newton method

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Authors: Sonia Sonia

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This paper presents a family of iterative scheme for solving nonlinear systems of equations which have wide application in sciences and engineering. The proposed iterative family is based upon some parameters which generates many different iterative schemes. This family is completely derivative free and uses first of divided difference operator. Moreover some numerical experiments are performed and compared with existing methods. Analysis of convergence shows that the presented family has fourth-order of convergence. The dynamical behaviour of proposed family and local convergence have also been discussed. The numerical performance and convergence region comparison demonstrates that proposed family is efficient.

Keywords: convergence, divided difference operator, nonlinear system, Newton's method

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Authors: M. Harmel, H. Khachai

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The first principles within the full potential linearized augmented plane wave (FP-LAPW) method were applied to study the structural and electronic properties of cubic perovskite-type compounds BiAlO3 and BiGaO3. The lattice constant, bulk modulus, its pressure derivative, band structure and density of states were obtained. The results show that BiGaO3 should exhibit higher hardness and stiffness than BiAlO3. The Al–O or Ga–O bonds are typically covalent with a strong hybridization as well as Bi–O ones that have a significant ionic character. Both materials are weakly ionic and exhibit wide and indirect band gaps, which are typical of insulators.

Keywords: DFT, Ab initio, electronic structure, Perovskite structure, ferroelectrics

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Authors: Kamel Al-Khaled

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In this paper, numerical solutions for the nonlinear coupled Korteweg-de Vries, (abbreviated as KdV) equations are calculated by Sinc-collocation method. This approach is based on a global collocation method using Sinc basis functions. First, discretizing time derivative of the KdV equations by a classic finite difference formula, while the space derivatives are approximated by a $\theta-$weighted scheme. Sinc functions are used to solve these two equations. Soliton solutions are constructed to show the nature of the solution. The numerical results are shown to demonstrate the efficiency of the newly proposed method.

Keywords: Nonlinear coupled KdV equations, Soliton solutions, Sinc-collocation method, Sinc functions

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Authors: Marcio Freire Cruz, Naoaki Ono, Shigehiko Kanaya, Carlos Arthur Mattos Teixeira Cavalcante

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The systems that record patient care information, known as Electronic Medical Record (EMR) and those that monitor vital signs of patients, such as heart rate, body temperature, and blood pressure have been extremely valuable for the effectiveness of the patient’s treatment. Several kinds of research have been using data from EMRs and vital signs of patients to predict illnesses. Among them, we highlight those that intend to predict, classify, or, at least identify patterns, of sepsis illness in patients under vital signs monitoring. Sepsis is an organic dysfunction caused by a dysregulated patient's response to an infection that affects millions of people worldwide. Early detection of sepsis is expected to provide a significant improvement in its treatment. Preceding works usually combined medical, statistical, mathematical and computational models to develop detection methods for early prediction, getting higher accuracies, and using the smallest number of variables. Among other techniques, we could find researches using survival analysis, specialist systems, machine learning and deep learning that reached great results. In our research, patients are modeled as points moving each hour in an n-dimensional space where n is the number of vital signs (variables). These points can reach a sepsis target point after some time. For now, the sepsis target point was calculated using the median of all patients’ variables on the sepsis onset. From these points, we calculate for each hour the position vector, the first derivative (velocity vector) and the second derivative (acceleration vector) of the variables to evaluate their behavior. And we construct a prediction model based on a Long Short-Term Memory (LSTM) Network, including these derivatives as explanatory variables. The accuracy of the prediction 6 hours before the time of sepsis, considering only the vital signs reached 83.24% and by including the vectors position, speed, and acceleration, we obtained 94.96%. The data are being collected from Medical Information Mart for Intensive Care (MIMIC) Database, a public database that contains vital signs, laboratory test results, observations, notes, and so on, from more than 60.000 patients.

Keywords: dynamic analysis, long short-term memory, prediction, sepsis

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Authors: Ali Oveysi Sarabi

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In this paper, controller design for the attitude and altitude dynamics of an outdoor quadrotor, which is constructed with low cost actuators and drivers, is aimed. Before designing the controller, the quadrotor is modeled mathematically in Matlab-Simulink environment. To control attitude dynamics, linear quadratic regulator (LQR) based controllers are designed, simulated and applied to the system. Two different proportional-integral-derivative action (PID) controllers are designed to control yaw and altitude dynamics. During the implementation of the designed controllers, different test setups are used. Designed controllers are implemented and tuned on the real system using xPC Target. Tests show that these basic control structures are successful to control the attitude and altitude dynamics.

Keywords: helicopter balance, flight dynamics, autonomous landing, control robotics

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Authors: Waroton Paisuwan, Mongkol Sukwattanasinitt, Mamoru Tobisu, Anawat Ajavakom

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Novel dihydroquinoline derivatives (DHP and DHP-OH) were synthesized in one pot via a tandem trimerization-cyclization of methylpropiolate. DHP and DHP-OH possess strong blue fluorescence with high quantum efficiencies over 0.70 in aqueous media. DHP-OH displays a remarkable fluorescence quenching selectively to the presence of Au3+ through the oxidation of dihydropyridine to pyridinium ion as confirmed by NMR and HRMS. DHP-OH was used to demonstrate the quantitative analysis of Au3+ in water samples with the limit of detection of 33 ppb and excellent recovery (>95%). This fluorescent probe was also applied for the determination of Au3+ residue in the gold nanoparticle solution and a paper-based sensing strip for the on-site detection of Au3+.

Keywords: Gold(III) ion detection, Fluorescent sensor, Fluorescence quenching, Dihydropyridine, Gold nanoparticles (AuNPs)

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Authors: Shradha S. Binani, Pravin S. Bodke, Ravi V. Joat

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An efficient method has been described for the synthesis of 6-(substituted aryl)-4-(2'- hydroxy-5'-chlorophenyl)-1, 6-dihydropyrimidine-2-thiol, as a beneficial antibacterial and antifungal agents. The diketones of title compounds were synthesized in four steps and subsequently these diketones were further reacted with thiourea in the presence of DMF, which led to the formation of dihydropyrimidine derivatives 5 (a-f). Compounds 5 (a-f) were screened for their in vitro antibacterial and antifungal activity by agar well method. Compounds 5b, 5c, 5e, and 5f were exhibited significant antimicrobial potential against tested strains at 50ug/ml and 100ug/ml concentrations. Six novel dihydropyrimidine analogues have been synthesized, characterized and found to be promising antibacterial and antifungal agents.

Keywords: diketones, dihyropyrimidine, antimicrobial activity, thiol group

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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: Pablo Martin, Jorge Olivares, Fernando Maass

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The use of fractional derivatives to different problems in Engineering and Physics has been increasing in the last decade. For this reason, we have here considered partial derivatives when the integral is a spherical Bessel function of the first kind in both regular and modified ones simple initial conditions have been also considered. In this way, the solution has been found as a combination of hypergeometric functions. The case of a general rational value for α of the fractional derivative α has been solved in a general way for alpha between zero and two. The modified spherical Bessel functions of the first kind have been also considered and how to go from the regular case to the modified one will be also shown.

Keywords: caputo fractional derivatives, hypergeometric functions, linear differential equations, spherical Bessel functions

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Authors: Sajeda Elbashabsheh, Kamel Al-Khaled

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This paper applies a modified Laplace Adomian decomposition method to solve the time-fractional JaulentMiodek system. The method produce convergent series solutions with easily compatible components. This paper considers the Caputo fractional derivative. The effectiveness and applicability of the method are demonstrated by comparing its results with those of prior studies. Results are presented in tables and figures. These solutions might be imperative and significant for the explanation of some practical physical phenomena. All computations and figures in the work are done using MATHEMATICA. The numerical results demonstrate that the current methods are effective, reliable, and simple to i implement for nonlinear fractional partial differential equations.

Keywords: approximate solutions, Jaulent-Miodek system, Adomian decomposition method, solitons

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Authors: Shield B. Lin, Sameer Abdali

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Computer simulations were performed using MATLAB/Simulink for a vibration isolation system for astronaut’s exercise platform. Simulation parameters initially were based on an on-going experiment in a laboratory at NASA Johnson Space Center. The authors expanded later simulations to include other parameters. A discrete proportional-integral-derivative controller with a low-pass filter commanding a linear actuator served as the active control unit to push and pull a counterweight in balancing the disturbance forces. A spring-damper device is used as an optional passive control unit. Simulation results indicated such design could achieve near complete vibration isolation with small displacements of the exercise platform.

Keywords: control, counterweight, isolation, vibration

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Authors: Li Dan, Zhao Junsuo, Zhang Wenjun

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Aiming at the shortcomings of the Quantum Genetic Algorithm such as the multimodal function optimization problems easily falling into the local optimum, and vulnerable to premature convergence due to no closely relationship between individuals, the paper presents an Improved Many Worlds Quantum Genetic Algorithm (IMWQGA). The paper using the concept of Many Worlds; using the derivative way of parallel worlds’ parallel evolution; putting forward the thought which updating the population according to the main body; adopting the transition methods such as parallel transition, backtracking, travel forth. In addition, the algorithm in the paper also proposes the quantum training operator and the combinatorial optimization operator as new operators of quantum genetic algorithm.

Keywords: quantum genetic algorithm, many worlds, quantum training operator, combinatorial optimization operator

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Authors: Gitanjali Pagare, Hansa Devi, S. P. Sanyal

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Full-potential linearized augmented plane wave (FLAPW) method has been employed within the generalized gradient approximation (GGA) and local spin density approximation (LSDA) as the exchange correlation potential to investigate elastic properties of LaX (X = Cd and Hg) in their B2-type (CsCl) crystal structure. The calculated ground state properties such as lattice constant (a0), bulk modulus (B) and pressure derivative of bulk modulus (B') agree well with the available experimental results. The second order elastic constants (C11, C12 and C44) have been calculated. The ductility or brittleness of these intermetallic compounds is predicted by using Pugh’s rule B/GH and Cauchy’s pressure (C12-C44). The calculated results indicate that LaHg is the ductile whereas LaCd is brittle in nature.

Keywords: ductility/brittleness, elastic constants, equation of states, FP-LAPW method, intermetallics

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Authors: Yalçın Kılıç, İbrahim Kani

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In recent years, interest in the synthesis of coordination compounds has greatly increased due to various application areas (such as catalysis, gas storage, luminescence). Dicarboxylic acids are often used in the synthesis of metal complexes. Bis-thiosalicylate derivative ligands contribute to the synthesis of structures of crystal engineering interest, as they can have both rigid and flexible properties. In addition, these ligands have great potential in terms of catalytic applications with the sulfur and oxygen donor atoms in their structures. In this study, we synthesized a Cu(II) complex [Cu(tsaxyl)(phen)2]•CH3OH (where tsaxyl = 2,2'-(1,2-phylenebis(methylene))bis(sulfanedyl)dibenzoate, phen = 1,10-phenantroline) and characterized through X-ray crystallography. The catalytic activities of Cu(II) complex on oxidation of ethylbenzene, cyclohexane, diphenylmethane, p-xylene were performed in acetonitrile with t-BuOOH as the source of oxygen.

Keywords: complex, crystallography, catalysis, oxidation

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Authors: Trilok Mathur, Shivi Agarwal

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This paper deals with the solutions of fuzzy-fractional-order Riccati equations under Caputo-type fuzzy fractional derivatives. The Caputo-type fuzzy fractional derivatives are defined based on Hukuhura difference and strongly generalized fuzzy differentiability. The Laplace-Adomian-Pade method is used for solving fractional Riccati-type initial value differential equations of fractional order. Moreover, we also displayed some examples to illustrate our methods.

Keywords: Caputo-type fuzzy fractional derivative, Fractional Riccati differential equations, Laplace-Adomian-Pade method, Mittag Leffler function

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Authors: Jafar Khodagholizadeh

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In this talk, we study the tensor mode equation of perturbation in the presence of nonzero $-\Lambda$ as dark energy, whose dynamic nature depends on the Hubble parameter $ H$ and/or its time derivative. Dark energy, according to the total vacuum contribution, has little effect during the radiation-dominated era, but it reduces the squared amplitude of gravitational waves (GWs) up to $60\%$ for the wavelengths that enter the horizon during the matter-dominated era. Moreover, the observations bound on dark energy models, such as running vacuum model (RVM), generalized running vacuum model (GRVM), and generalized running vacuum subcase (GRVS), are effective in reducing the GWs’ amplitude. Although this effect is less for the wavelengths that enter the horizon at later times, this reduction is stable and permanent.

Keywords: gravitational waves, dark energy, GW's amplitude, all stage universe

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Authors: Yacine Arioua

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In this paper, we investigate the existence and uniqueness of solutions for a coupled system of nonlinear Caputo-type Katugampola fractional differential equations with integral boundary conditions. Based upon a contraction mapping principle, Schauders fixed point theorems, some new existence and uniqueness results of solutions for the given problems are obtained. For application, some examples are given to illustrate the usefulness of our main results.

Keywords: fractional differential equations, coupled system, Caputo-Katugampola derivative, fixed point theorems, existence, uniqueness

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