Numerical treatment for solving the perturbed fractional PDEs using hybrid techniques

In this article, an accurate numerical approach is introduced. In this approach we mixed between the fractional finite difference method and the restrictive Taylor approximation (RTA). The proposed method is implemented to solve numerically the perturbed fractional partial differential equations (FPDEs). Special attention is given to study the stability and consistency of the method by means of Gerschgorin theorem and using the stability matrix analysis. Two numerical examples are given and compared with the exact solution.