This paper is concerned with the study of the quenching behavior of the solution for the following initial-boundary value problem:

where  is bounded and symmetric function.  is the “conformable fractional derivative” of u in relation to the time variable of order α defined as follows:

for all

We find the numerical quenching solution for a fractional order equation with homogeneous Dirichlet boundary conditions and show that the quenching occurs on the boundary. Also, we find some additional conditions on the initial data, and the dimension of the domain under which the numerical solution of our problem quenches, estimate the numerical quenching time and establish a convergence result for this quenching time. Finally, we give some numerical results to illustrate our analysis.

reaction diffusion equation, quenching solution, conformable fractional derivatives, convergence, numerical quenching time, extinction, numerical quenching time, existence, finite difference method.

Received: April 2, 2023;  Accepted: May 25, 2023; Published: September 5, 2023

How to cite this article: D. Yekre Benjamn, Yoro Gozo, Diopina Kambere and Halima Nachid, Perturbed quenching phenomenon for a conformable fractional order reaction-diffusion equation, Universal Journal of Mathematics and Mathematical Sciences 19(1) (2023), 61-85. http://dx.doi.org/10.17654/2277141723017

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

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