Work

An effective numerical method for solving fractional delay differential equations using fractional-order Chelyshkov functions

Year: 2024

Type: article

Abstract: In this paper, the fractional-order Chelyshkov functions (FCHFs) and Riemann-Liouville fractional integrals are utilized to find numerical solutions to fractional delay differential equations, by transforming the problem into a system of algebraic equations with unknown FCHFs coefficients. An error bound of FCHFs approximation is estimated and its convergence is also demonstrated. The effectiveness and accuracy of the presented method are established through several examples. The resulting solution is accurate and agrees with the exact solution, even if the exact solution is not a polynomial. Moreover, comparisons between the obtained numerical results and those recently reported in the literature are shown.

Source: Boundary Value Problems

DOI: 10.1186/s13661-024-01913-8

Authors: A. I. Ahmed, M. S. Al-Sharif

Institution: Al-Azhar University

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,790

Funder: Al-Azhar University