Sami Baroudi, Abderrazak Kassidi, Ali El Mfadel, M’hamed Elomari, An accurate and stable numerical scheme for fractional integro-differential equations

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DOI: 10.23952/jano.8.2026.3.04
Volume 8, Issue 3, 1 December 2026, Pages 373-394

Abstract. This paper investigates a novel compact finite difference scheme for numerical solutions of a class of nonlinear $\Upsilon$ -Caputo time-fractional integro-differential equations. The fractional derivative and integral are discretized in time by using the L1 approximation, while the nonlinear convection term is approximated by a specially designed nonlinear compact difference operator. A rigorous theoretical analysis establishes the unconditional stability and convergence of the proposed method. Numerical experiments are presented to support the theoretical results and demonstrate the accuracy and computational efficiency of the scheme across various test scenarios.

How to Cite this Article:
S. Baroudi, A. Kassidi, A. El Mfadel, M. Elomari, An accurate and stable numerical scheme for fractional integro-differential equations, J. Appl. Numer. Optim. 8 (2026), 373-394.