Work

A Spectral Approach to Variable-Order Fractional Differential Equations: Improved Operational Matrices for Fractional Jacobi Functions

Year: 2025

Type: article

Abstract: The current paper presents a novel numerical technique to handle variable-order multiterm fractional differential equations (VO-MTFDEs) supplemented with initial conditions (ICs) by introducing generalized fractional Jacobi functions (GFJFs). These GFJFs satisfy the associated ICs. A crucial part of this approach is using the spectral collocation method (SCM) and building operational matrices (OMs) for both integer-order and variable-order fractional derivatives in the context of GFJFs. These lead to efficient and accurate computations. The suggested algorithm’s convergence and error analysis are proved. The feasibility of the suggested procedure is confirmed via five numerical test examples.

Source: Mathematics

DOI: 10.3390/math13162544

Authors: Hany M. Ahmed, Mohammad Izadi, Carlo Cattani

Institutions: Helwan University, Shahid Bahonar University of Kerman, Università degli Studi della Tuscia

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

OpenAlex ID: W4413121349

FWCI: 5.158

Cites: 61

Cited by: 7

Related to: 10