Solving the fractional integro-differential equations using fractional order Jacobi polynomials
Authors
Abstract:
In this paper, we are intend to present a numerical algorithm for computing approximate solution of linear and nonlinear Fredholm, Volterra and Fredholm-Volterra integro-differential equations. The approximated solution is written in terms of fractional Jacobi polynomials. In this way, firstly we define Riemann-Liouville fractional operational matrix of fractional order Jacobi polynomials, then by using this matrix and the least squares method the solution of equation reduce to a system of algebraic equations which is solved through the Newton’s iterative method. In the next step we analyze convergence of the solution, and then to confirm the theoretical issue we examine some numerical examples. The results indicate the accuracy and efficiency of the method. The excellence of this method is its generality, which includes the fractional order Legendre and Chebyshev polynomials. Also it is also easy to use for linear and nonlinear integro-differential equations and provides good results.
similar resources
A spectral method based on Hahn polynomials for solving weakly singular fractional order integro-differential equations
In this paper, we consider the discrete Hahn polynomials and investigate their application for numerical solutions of the fractional order integro-differential equations with weakly singular kernel .This paper presented the operational matrix of the fractional integration of Hahn polynomials for the first time. The main advantage of approximating a continuous function by Hahn polynomials is tha...
full textFractional type of flatlet oblique multiwavelet for solving fractional differential and integro-differential equations
The construction of fractional type of flatlet biorthogonal multiwavelet system is investigated in this paper. We apply this system as basis functions to solve the fractional differential and integro-differential equations. Biorthogonality and high vanishing moments of this system are two major properties which lead to the good approximation for the solutions of the given problems. Some test pr...
full textSolving two-dimensional fractional integro-differential equations by Legendre wavelets
In this paper, we introduce the two-dimensional Legendre wavelets (2D-LWs), and develop them for solving a class of two-dimensional integro-differential equations (2D-IDEs) of fractional order. We also investigate convergence of the method. Finally, we give some illustrative examples to demonstrate the validity and efficiency of the method.
full textfractional type of flatlet oblique multiwavelet for solving fractional differential and integro-differential equations
the construction of fractional type of flatlet biorthogonal multiwavelet system is investigated in this paper. we apply this system as basis functions to solve the fractional differential and integro-differential equations. biorthogonality and high vanishing moments of this system are two major properties which lead to the good approximation for the solutions of the given problems. some test pr...
full textLegendre Wavelets for Solving Fractional Differential Equations
In this paper, we develop a framework to obtain approximate numerical solutions to ordinary differential equations (ODEs) involving fractional order derivatives using Legendre wavelets approximations. The continues Legendre wavelets constructed on [0, 1] are utilized as a basis in collocation method. Illustrative examples are included to demonstrate the validity and applicability of the techn...
full textMy Resources
Journal title
volume 8 issue 4
pages 0- 0
publication date 2022-12
By following a journal you will be notified via email when a new issue of this journal is published.
No Keywords
Hosted on Doprax cloud platform doprax.com
copyright © 2015-2023