In this article, we study the fractional diffusion equation with spatial Riesz fractional derivative. The continuation of the solution of this fractional equation to the solution of the corresponding integer order equation is proved. The series solution is obtained based on properties of Riesz fractional derivative operator and utilizing the optimal homotopy analysis method (OHAM). Numerical simulations are presented to validate the method and to show the effect of changing the fractional derivative parameter on the solution behavior.
Elsaid, A.; Shamseldeen, S.; and Madkour, S.
Iterative Solution of Fractional Diffusion Equation Modelling Anomalous Diffusion,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 11,
2, Article 21.
Available at: https://digitalcommons.pvamu.edu/aam/vol11/iss2/21