In this work, we utilized the nonsingular kernel fractional derivative, known as Caputo-Fabrizio fractional derivative, to solve for the numerical solution of two-dimensional space-time fractional diffusion equation using finite difference approximation. Analysis for unconditional stability and convergence have been presented. Interestingly, by using the nonsingular kernel fractional derivative, it is found that the convergence generates a second order accuracy weighted by the memory kernel of the fractional derivative. In addition, fractional order dependency of the convergence have been discussed and compared to some previous works. Moreover, the obtained finite difference approximation method was employed to solve for a given example. Numerical test verified the analysis of this study.
Digital Object Identifier (DOI)
A. Rangaig, Norodin and Alem G. Pido, Alvanh
"Finite Difference Approximation Method for Two- Dimensional Space-Time Fractional Diffusion Equation Using Nonsingular Fractional Derivative,"
Progress in Fractional Differentiation & Applications: Vol. 5
, Article 5.
Available at: https://dc.naturalspublishing.com/pfda/vol5/iss4/5