We present a numerical algorithm for time-fractional reaction-diffusion equation with boundary condition to find approximate solutions by using perturbation method. We study the quenching behavior with the conformable Euler method (CEM) for the finite difference discretization of the fractional derivative in the Caputo sense for the following initial-boundary value problem:

where  is a bounded domain in  with smooth boundary   is a bounded and symmetric function.  is the “conformable fractional derivative” of u with respect to the time variable of order   in the sense of Caputo. Also, we study the numerical quenching solution for a fractional diffusion equation with degenerate source term. The fractional derivative, acting on the spatial variable, contains left-sided Caputo derivative and right-sided Riemann-Liouville derivative simultaneously.

reaction diffusion equation, quenching solution, conformable fractional derivatives (CFD), conformable Euler method (CEM), modified conformable Euler method (MCEM), perturbation method, analytical solution, homotopy perturbation method, convergence, numerical quenching time, extinction, existence, finite difference method, Maple, MATLAB-Simulink.

Received: May 31, 2024; Revised: June 14, 2024; Accepted: November 28, 2024; Published: January 6, 2025

How to cite this article: Kambire D. Gnowille, HALIMA NACHID and ALI S. SAMUEL FARMA, The perturbed numerical process for a reaction-diffusion problem with conformable derivative, International Journal of Numerical Methods and Applications 25(1) (2025), 103-132. https://doi.org/10.17654/0975045225005

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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