Try Laplace or Fourier transform method to reduce problem to algebraic.

This article aims to develop a direct numerical approach to solve the space-fractional partial differential equations (PDEs) based on a new differential quadrature (DQ) technique. The fractional derivatives are approximated by the weighted linear combinations of the function values at discrete grid points on problem domain with the weights calculated via using three types of radial basis functions (RBFs) as test functions. The method in presence is robust, straight forward to apply, and highly accurate under the condition that the shape parameters of RBFs are well chosen. Numerical tests are provided to illustrate its validity and capability.

Article Numerical solution of space-fractional partial differential ...

Try Laplace or Fourier transform method to reduce problem to algebraic.

finite element, finite difference methods

I think that the following book that provides efficient and reliable numerical methods for solving FODEs and FPDEs can be useful for your question.

https://www.researchgate.net/publication/325170548_Numerical_methods_for_fractional_calculus

finite difference techniques are reliable techniques for solving reaction-diffusion problems.

Use Laplace transform with iterative methods to solve these problems.

We can't say which of these mentioned methods is the best, since that depends on the nature of initial-boundary conditions associated with the problem. Moreover, the type of programming that will be used to compute the numerical solutions.

Exactly@Maan A. Rasheed, I agree because we have to check the convergence of the method and accuracy of the results with minimum computational efforts.

Dear Dr. Miled El Hajji,

To find the Best method to solve 2D space-fractional partial differential equation go through following research paper links.

01. Article Finite difference methods for two-dimensional fractional dis...

02. Article Differential quadrature method for space-fractional diffusio...

03. Article A numerical scheme based on Bernoulli wavelets and collocati...

04. Article New Algorithm based on Shifted Legendre Polynomials for Frac...

05. Article A Parallel Algorithm for the Two-Dimensional Time Fractional...

06. Article Similarity solution to fractional nonlinear space-time diffu...

I hope I have answered your question.

With Best Wishes,

Samir G. Pandya

While not as precise, a cute way to solve/check your answer is to put it on a spread sheet like Excel. We use to solve 2D Laplace boundary value problems in Cartesian coordinates this way fixing the boundary values along the borders and then varying the number of row and columns to achieve accuracy.

I think, homotopy analysis method is better than other methods because of its flexibility. I have some papers based on this topic. Please check my papers.