Work

Collocation method for fractional differential equations using hybrid fractional-order Chelyshkov functions

Year: 2025

Type: article

Abstract: In this paper, we introduce a new numerical method based on the hybrid of fractional-order Chelyshkov functions and block-pulse functions for solving fractional differential equations. The fractional derivatives are considered in the Caputo sense. The exact formula for the Riemann-Liouville fractional integral of these basis functions is derived via the Laplace transform. This formula, together with the spectral collocation method are used to reduce the main problem to a system of algebraic equations. The convergence of the introduced method is discussed. Several illustrative examples are included to demonstrate the accuracy and applicability of the proposed method.

Source: Boundary Value Problems

DOI: 10.1186/s13661-025-02124-5

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

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: $1,890

Funder: Al-Azhar University