Robust Approximation for Non-Linear Variable-Distributed Fractional Differential Equation with Non-Smooth Solutions

Authors

A. Emin Department of Software Engineering, Istanbul Gelisim University, Istanbul, 34310, Turkey
M. A. Abdelkawy Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia https://orcid.org/0000-0002-9043-9644
Anjan Biswas Department of Mathematics and Physics, Grambling State University, Grambling, LA, 71245-2715, USA https://orcid.org/0000-0002-8131-6044

DOI:

https://doi.org/10.37256/cm.6620257643

Keywords:

caputo fractional of variable order, spectral collocation method, distributed fractional, fractional Riccati differential equation, shifted Legendre polynomials

Abstract

This article introduces a spectral method aimed at estimating solutions for nonlinear Variable Distributed-Order Fractional Differential Equations (VDO-FDEs) with a non-smooth solution in one-dimensional and time-nonlinear VDOFDEs. Initially, we express the solution and its fractional derivatives using a series of Shifted Legendre Polynomials (SLPs). Subsequently, the expansion coefficients were derived by transforming the VDO-FDEs in addition to the conditions related to the algebraic system. We illustrate effectiveness and feasibility through various numerical tests.

Downloads

Published

2025-11-26

Issue

Contemporary Mathematics, Volume 6 Issue 6 (2025)

Section

Research Article

License

This work is licensed under a Creative Commons Attribution 4.0 International License.