Solving time-fractional differential diffusion equation by theta-method

This paper proposes a numerical method to deal with the one-dimensional time-fractional diffusion equation defined by Caputo fractional derivative. The paper aims to present a general framework of the θ −method for solving time-fractional diffusion differential equations for (0 ≤ θ ≤ 1). Consistency, stability and convergence analysis of the method is discussed. Finally, the obtained results reveal that the proposed technique is very effective, convenient and quite accurate to such considered problems.

Fractional PDE (FPDE), Finite differences