In this paper, a class of constrained fractional optimization problems under a dynamic system involving the yr-Caputo fractional derivative is introduced. A computational method based on the modifiedhat basis functio...
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In this paper, a class of constrained fractional optimization problems under a dynamic system involving the yr-Caputo fractional derivative is introduced. A computational method based on the modifiedhat basis functions is developed to solve these problems. This work is done by obtaining a new operational matrix for the yr-Riemann-Liouville fractional integral of the modified hat functions. The established approach utilizes the modified hat functions to approximate the state and control variables, successfully converting the main problem into a set of algebraic equations. This method provides a systematic and efficient way to obtain numerical solutions for this class of problems. Several test problems are examined to verify the accuracy and applicability of the proposed method.
We introduce a numerical method, based on modified hat functions, for solving a class of fractional optimal control problems. In our scheme, the control and the fractional derivative of the state function are consider...
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We introduce a numerical method, based on modified hat functions, for solving a class of fractional optimal control problems. In our scheme, the control and the fractional derivative of the state function are considered as linear combinations of the modified hat functions. The fractional derivative is considered in the Caputo sense while the Riemann-Liouville integral operator is used to give approximations for the state function and some of its derivatives. To this aim, we use the fractional order integration operational matrix of the modified hat functions and some properties of the Caputo derivative and Riemann-Liouville integral operators. Using results of the considered basis functions, solving the fractional optimal control problem is reduced to the solution of a system of nonlinear algebraic equations. An error bound is proved for the approximate optimal value of the performance index obtained by the proposed method. The method is then generalized for solving a class of fractional optimal control problems with inequality constraints. The most important advantages of our method are easy implementation, simple operations, and elimination of numerical integration. Some illustrative examples are considered to demonstrate the effectiveness and accuracy of the proposed technique. (C) 2019 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.
The present work is devoted to proposing a low-cost spectral method based on the modified hat functions for solving fractional delay differential equations. The fractional derivative is considered in the sense of Capu...
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The present work is devoted to proposing a low-cost spectral method based on the modified hat functions for solving fractional delay differential equations. The fractional derivative is considered in the sense of Caputo. In order to solve the considered problem, the existing functions in it are approximated using the basis functions. By employing some important properties of the basis functions, Caputo derivative and Riemann-Liouville fractional integral, the main problem is transformed into some systems of nonlinear algebraic equations including two unknown parameters. This procedure mainly simplifies the problem and gives its approximate solution after solving the resulting systems. In addition, the computational complexity of the derived system is investigated. An error analysis is discussed to show the convergence order of the method. Finally, the suggested technique is applied to some sample problems with the aim of checking its validity and accuracy. (C) 2022 Elsevier B.V. All rights reserved.
In this paper, a linear combination of quadratic modified hat functions is proposed to solve stochastic Ito-Volterra integral equation with multi-stochastic terms. All known and unknown functions are expanded in terms...
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In this paper, a linear combination of quadratic modified hat functions is proposed to solve stochastic Ito-Volterra integral equation with multi-stochastic terms. All known and unknown functions are expanded in terms of modified hat functions and replaced in the original equation. The operational matrices are calculated and embedded in the equation to achieve a linear system of equations which gives the expansion coefficients of the solution. Also, under some conditions the error of the method is O(h(3)). The accuracy and reliability of the method are studied and compared with those of block pulse functions and generalized hatfunctions in some examples.
In this paper, a new numerical approach is developed for solving linear and nonlinear Volterra-Fredholm integral equations. The fundamental structure of the presented method is based on the modification of hat functio...
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In this paper, a new numerical approach is developed for solving linear and nonlinear Volterra-Fredholm integral equations. The fundamental structure of the presented method is based on the modification of hatfunctions. The properties of modification of hatfunctions (MHFs) are first presented. After implementation of our scheme, the solution of the main problem would be transformed into the solution of a system of linear or nonlinear algebraic equations. Also, an error analysis is provided under several mild conditions. In addition, examples are presented to illustrate the pertinent features of the method and the results are discussed. (C) 2016 Elsevier Inc. All rights reserved.
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