International Journal of Research and Innovation in Applied Science (IJRIAS)
Advancing Solutions for Fractional Volterra–Fredholm Integro-Differential Equations: A Comprehensive Review of Recent Numerical Methods
Published June 30, 2026 • Vol. 11, Issue 6, pp. 1604–1620Open Access
DOI: 10.51584/IJRIAS.2026.11060125
Abstract
Fractional Volterra–Fredholm integro differential equations (FVFIDEs) combine fractional derivatives with nonlocal Volterra and Fredholm operators, making them a central tool for modeling systems with memory and spatial interactions. Analytical solutions are rare, and numerical methods have become essential for practical applications. This review synthesizes recent advances in numerical approaches, including predictor–corrector schemes, spectral methods, iterative algorithms, and hybrid techniques. Emphasis is placed on convergence analysis, computational efficiency, and comparative performance. By consolidating developments from 2020–2025, the article provides a structured overview of current solution strategies and highlights open challenges, offering guidance for researchers seeking effective tools to advance the study of FVFIDEs.
Keywords: Fractional calculus; Volterra–Fredholm equations; Integro differential equations; Numerical methods; Spectral techniques; Predictor–corrector schemes; Convergence analysis; Applied mathematics
| Journal | International Journal of Research and Innovation in Applied Science (IJRIAS) |
|---|---|
| ISSN | 2454-6194 |
| Volume / Issue | Volume 11, Issue 6 |
| Pages | 1604–1620 |
| Publication date | June 30, 2026 |
| DOI | 10.51584/IJRIAS.2026.11060125 |
| Publisher | RSIS International |
| License | Open Access |
How to cite this article
Ali Karim Lelo Alobaidi (2026). Advancing Solutions for Fractional Volterra–Fredholm Integro-Differential Equations: A Comprehensive Review of Recent Numerical Methods. International Journal of Research and Innovation in Applied Science (IJRIAS), 11(6), 1604-1620. https://doi.org/10.51584/IJRIAS.2026.11060125
BibTeX
@article{Ali2026,
title = {Advancing Solutions for Fractional Volterra–Fredholm Integro-Differential Equations: A Comprehensive Review of Recent Numerical Methods},
author = {Ali Karim Lelo Alobaidi},
journal = {International Journal of Research and Innovation in Applied Science (IJRIAS)},
volume = {11},
number = {6},
pages = {1604--1620},
year = {2026},
doi = {10.51584/IJRIAS.2026.11060125},
publisher = {RSIS International}
}