Modeling and Numerical Investigation of Space-Fractional Advection Diffusion Models by Galerkin’s Weighted Residual Method

Muhammad Hakim Ali Qasmi, Syed Ali Mohsin Bukhari, Amal Alshabanat and Umair Ali

Journal of Mathematics, 2026, vol. 2026, 1-10

Abstract: In this study, we first model the space-fractional advection equation by choosing an exact solution under certain restrictions. Then, the forcing term is determined according to that solution. Secondly, we present a numerical solution for a class of space-fractional advection-diffusion equations with a nonlinear source term involving both time and space variables, using the Galerkin weighted residual method. Bernoulli polynomials are employed as the basis functions, and fractional derivatives are considered in the Caputo sense. The initial solution guesses are obtained through the Galerkin projection method to solve the resulting system of matrix equations corresponding to all basis terms. Furthermore, the equation is solved for both the steady-state and particular solutions using matrix exponentiation and the variation-of-parameters method, respectively. Finally, examples are provided to verify the proposed model and numerical approach. The proposed method is easy to implement and demonstrates high accuracy for such space-fractional models.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:9205345

DOI: 10.1155/jom/9205345

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