Title: Numerical solutions for high-order fractional local initial boundary value problems

Authors: Rachid Belgacem; Ahmed Bokhari; Salih Djilali; Djelloul Ziane

Addresses: Faculty of Exact Sciences and Informatics, Mathematic Department, Hassiba Benbouali University, Chlef, Algeria; Laboratory of Mathematics and Its Applications LMA, Hassiba Benbouali University, Chlef, Algeria ' Faculty of Exact Sciences and Informatics, Mathematic Department, Hassiba Benbouali University, Chlef, Algeria; Laboratory of Mathematics and Its Applications LMA, Hassiba Benbouali University, Chlef, Algeria ' Faculty of Exact Sciences and Informatics, Mathematic Department, Hassiba Benbouali University, Chlef, Algeria ' Laboratory of Mathematics and Its Applications (LAMAP), University of Oran 1, Oran, Algeria

Abstract: The primary objective of this research is to employ the local fractional Sumudu transform decomposition method (LFSTDM) for solving higher-dimensional linear and nonlinear initial boundary value problems (IBVP) characterised by variable coefficients and fractional local derivatives. The findings demonstrate the efficacy of this method in deriving non-differentiable solutions for established problems involving local fractional derivatives. By effectively reducing computational workload, the LFSTDM emerges as a promising approach for addressing such challenges. The following problem is considered: L_mσU (r, τ) + R_σU(r, τ) + N_σU(r, τ) = g(r, τ).

Keywords: initial boundary value problem; local fractional derivative; Sumudu transform.

DOI: 10.1504/IJDSDE.2025.151443

International Journal of Dynamical Systems and Differential Equations, 2025 Vol.14 No.6, pp.544 - 564

Received: 25 May 2024
Accepted: 27 Sep 2024
Published online: 30 Jan 2026 *

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