Work

Exact and High-accuracy Solutions to Fractional Burgers-type and Reaction-diffusion Equations Using the Laplace-sba Method

Year: 2026

Type: article

Abstract: This paper applies the hybrid Laplace-SBA (Somé-Blaise-Abbo) method to solve three classes of nonlinear fractional partial differential equations with respect to time in the Caputo sense: a fourth-order viscoelastic wave model, a reaction-advection-diffusion system, and a Burgers-type equation with time-variable coefficients. By coupling the Laplace transform with successive approximations based on the fixed-point principle, the scheme avoids linearization, spatial discretization, and the computation of Adomian polynomials. The exact solutions for the first two models are obtained in a single iteration. For the fractional Burgers equation, the series approximations converge continuously to the classical solution as \(\alpha \rightarrow 2\), achieving absolute errors as low as \(10^{-18}\). These results demonstrate the efficiency and reliability of the Laplace-SBA method for nonlinear systems with memory effects.

Source: International Journal of Numerical Methods and Applications

DOI: 10.17654/69881125

Authors: BAYALLA Bazoboué Laurent, SAWADOGO Salomond, Jérémie Yiyuréboula BATIONO, Francis BASSONO

Institutions: Université Joseph Ki-Zerbo, Institut de Recherche Agronomique de Guinée

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

OpenAlex ID: W7222888044

FWCI:

Cites:

Cited by:

Related to: