Numerical Investigation of Fredholm Fractional Integro-differential Equations by Least Squares Method and Compact Combination of Shifted Chebyshev Polynomials-Reference-Cited by-同舟云学术

Numerical Investigation of Fredholm Fractional Integro-differential Equations by Least Squares Method and Compact Combination of Shifted Chebyshev Polynomials

Published:2023-07-18 Issue: Volume: Page:
ISSN:1776-0852
Container-title:Journal of Nonlinear Mathematical Physics
language:en
Short-container-title:J Nonlinear Math Phys

Author:

Benzahi Ahlem,Arar Nouria,Abada Nadjet,Rhaima Mohamed,Mchiri Lassaad,Makhlouf Abdellatif Ben

Abstract

AbstractIn this study, linear Fredholm fractional integro-differential equations (FIDEs) are numerically solved, where the fractional derivative is considered in the Caputo sense. In this work, the least squares method (LSM) using a compact combination of shifted Chebyshev polynomials (SCP) of the first Kind is applied to solving a class of FIDEs. Our aim is to write the unknown function as a series of a linear combination of SCP, and then to reduce the problem to a system of linear algebraic equations, which will be solved for the unknown constants associated with the approximate solution, using MATLAB R2020a. Finally, numerical examples are presented to confirm the reliability, applicability, and efficiency of this method, in addition, various comparisons are also shown.

Funder

King Saud University

Publisher

Springer Science and Business Media LLC

Subject

Mathematical Physics,Statistical and Nonlinear Physics

Link

https://link.springer.com/content/pdf/10.1007/s44198-023-00128-2.pdf

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