The primary focus of this study is to examine delay optimization problems, subject to a dynamical system that involves (Formula presented.) -Caputo fractional derivative. The generalized hat functions are applied to d...
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In this paper, operational matrix method based on the generalized hat functions is introduced for the approximate solutions of linear and nonlinear fractional integro-differential equations. The fractional order gener...
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In this paper, operational matrix method based on the generalized hat functions is introduced for the approximate solutions of linear and nonlinear fractional integro-differential equations. The fractional order generalized hat functions operational matrix of integration is also introduced. The linear and nonlinear fractional integro-differential equations are transformed into a system of algebraic equations. In addition, the method is presented with error analysis. Numerical examples are included to demonstrate the validity and applicability of the approach.
In conjunction with least squares method and generalized hat functions, we propose a new algorithm for stochastic Ito-Volterra integral equations. Firstly, the original problem is turned into solving a linear system o...
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In conjunction with least squares method and generalized hat functions, we propose a new algorithm for stochastic Ito-Volterra integral equations. Firstly, the original problem is turned into solving a linear system of equations. Further, an efficient strategy is constructed to figure out the relevant coefficients of the linear system of equations. For computation purposes, throughout this paper, stochastic Ito integrals are transformed into conventional integrals using integration by parts formula. We also theoretically examine the convergence of the proposed approach. In the end, we provide two related examples to verify the reliability and accuracy of our proposed method. And in comparison with their numerical errors of the traditional block pulse method, the error of our presented approach is smaller.
The purpose of this paper is to present a new and efficient computational method based on the hybrid of block-pulse functions and shifted Legendre polynomials together with their exact operational vector of integratio...
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The purpose of this paper is to present a new and efficient computational method based on the hybrid of block-pulse functions and shifted Legendre polynomials together with their exact operational vector of integration and stochastic operational matrix of integration with respect to the multifractional Brownian motion to approximate solutions of a class of nonlinear stochastic differential equations driven by multifractional Gaussian noise. The presented method transforms problems under consideration into systems of nonlinear equations which can be simply solved by the Newton method. Moreover, the convergence analysis of the presented method is investigated. Finally, the efficiency of the new method is illustrated by solving the stochastic logistic equation and three test problems.
In this paper, we propose a new numerical algorithm for solving linear and non linear fractional differential equations based on our newly constructed integer order and fractional order generalized hat functions opera...
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In this paper, we propose a new numerical algorithm for solving linear and non linear fractional differential equations based on our newly constructed integer order and fractional order generalized hat functions operational matrices of integration. The linear and nonlinear fractional order differential equations are transformed into a system of algebraic equations by these matrices and these algebraic equations are solved through known computational methods. Further some numerical examples are given to illustrate and establish the accuracy and reliability of the proposed algorithm. The results obtained, using the scheme presented here, are in full agreement with the analytical solutions and numerical results presented elsewhere. (C) 2012 Elsevier B. V. All rights reserved.
We propose a new spectral method, based on two classes of hatfunctions, for solving systems of fractional differential equations. The fractional derivative is considered in the Caputo sense. Properties of the basis f...
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We propose a new spectral method, based on two classes of hatfunctions, for solving systems of fractional differential equations. The fractional derivative is considered in the Caputo sense. Properties of the basis functions, Caputo derivatives and Riemann-Liouville fractional integrals, are used to reduce the main problem to a system of nonlinear algebraic equations. By analyzing in detail the resulting system, we show that the method needs few computational efforts. Two test problems are considered to illustrate the efficiency and accuracy of the proposed method. Finally, an application to a recent mathematical model in epidemiology is given, precisely to a system of fractional differential equations modeling the respiratory syncytial virus infection.
In this research study, we present an efficient method based on the generalized hat functions for solving nonlinear stochastic differential equations driven by the multi-fractional Gaussian noise. Based on the general...
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In this research study, we present an efficient method based on the generalized hat functions for solving nonlinear stochastic differential equations driven by the multi-fractional Gaussian noise. Based on the generalized hat functions, we derive a stochastic operational matrix of the integral operator with respect to the variable order fractional Brownian motion, for the first time so far. Also, we establish a procedure to generate the variable order fractional Brownian motion. Then, we use them to provide numerical solutions for the proposed problems. In addition, the convergence of the new method is theoretically analyzed. Moreover, we solve the stochastic logistic equation, stochastic population growth model, and three test problems to confirm the efficiency of the new method. The obtained results are compared with other existing methods used for solving these problems. (C) 2022 Elsevier Inc. All rights reserved.
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