Kareem A. Bello; Julius T. Adepoju

A Novel Double Mohand-Generalized ARA Transform Coupled with Adomian Decomposition Method for Multi-Dimensional Fractional Partial Differential Equations

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Author(s)

Kareem A. Bello ^1,* Julius T. Adepoju ¹

1. Department of Mathematics, Faculty of Physical Sciences, University of Ilorin, Kwara, Nigeria

* Corresponding author.

DOI: https://doi.org/10.5815/ijmsc.2026.02.01

Received: 30 Nov. 2025 / Revised: 20 Jan. 2026 / Accepted: 10 Mar. 2026 / Published: 8 Jun. 2026

Index Terms

Fractional Partial Differential Equations, Double Mohand Transform, Generalized ARA Transform, Adomian Decomposition Method, Mittag-Leffler Function, Banach Fixed-Point Theorem, Population Model

Abstract

The present research aims to introduce a brand new theoretical framework for solving multi-dimensional fractional partial differential equations (FPDEs) by developing a novel integral transform tool called the Double Mohand-Generalized ARA Transform (DM-GART). The DM-GART is a triple-integral operator that applies the Mohand transform twice—once in each spatial variable x and y and the ARA transform once in the temporal variable t; the adjective “Double” refers specifically to the double spatial application of the Mohand transform. The theoretical properties and existence/uniqueness results of this newly developed integral transform are rigorously established in a Banach fixed-point theorem setting. The newly developed integral transform tool is then synergistically combined with the Adomian Decomposition Method (ADM) to produce a novel technique called the Coupled Double Mohand-Generalized ARA Decomposition Method (CDM-GADM). The CDM-GADM is applied for solving generalised fractional biological population equations. The technique is assessed by comparing exact solutions with N-term series solutions for N = 4, 6, and 8. From the results obtained in Tables 3–10, it can be noted that with an increase in the terms from N = 4 to N = 8, the absolute errors decrease several orders of magnitude; the absolute errors for N = 8 are as low as 10⁻¹⁰ for α = 1.0 at smaller values of time. The results are obtained in the form of convergent series characterized by the Mittag-Leffler function, validating the efficiency of the proposed method. A tolerance of ε = 10⁻⁶ is used as the practical stopping criterion.

Cite This Paper

Kareem A. Bello, Julius T. Adepoju, "A Novel Double Mohand-Generalized ARA Transform Coupled with Adomian Decomposition Method for Multi-Dimensional Fractional Partial Differential Equations", International Journal of Mathematical Sciences and Computing(IJMSC), Vol.12, No.2, pp. 1-18, 2026. DOI: 10.5815/ijmsc.2026.02.01

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International Journal of Mathematical Sciences and Computing (IJMSC)