Stability of solutions of a class of nonlinear fractional diffusion equations with respect to a pseudo‐differential operator

Abstract

In this paper, we study the forward and the backward in time problems for a class of nonlinear diffusion equations with respect to the pseudo‐differential operator. Herein, we investigate the stability of the solution of the forward problem in relationship with parameters of the pseudo‐differential operator and initial data. Besides, as known, the backward in time problem is instability. Hence, we give a method to regularize the solution of the backward problem in the case of the parameters are perturbed.

On a multi‐point p$$ p $$‐Laplacian fractional differential equation with generalized fractional derivatives

“…The approach considered in the current paper is essentially new and has been rarely considered in the literature; the readers can consult relevant papers. [32][33][34][35][36]…”

“…We design a simulative numerical example to confirm the validity of the theoretical findings. The approach considered in the current paper is essentially new and has been rarely considered in the literature; the readers can consult relevant papers 32–36 …”