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Full-Text Articles in Analysis
Iterative Solution Of Fractional Diffusion Equation Modelling Anomalous Diffusion, A. Elsaid, S. Shamseldeen, S. Madkour
Iterative Solution Of Fractional Diffusion Equation Modelling Anomalous Diffusion, A. Elsaid, S. Shamseldeen, S. Madkour
Applications and Applied Mathematics: An International Journal (AAM)
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.
An Approximate Analytical Solution Of The Fractional Diffusion Equation With External Force And Different Type Of Absorbent Term - Revisited, S. Das, R. Kumar, P. K. Gupta
An Approximate Analytical Solution Of The Fractional Diffusion Equation With External Force And Different Type Of Absorbent Term - Revisited, S. Das, R. Kumar, P. K. Gupta
Applications and Applied Mathematics: An International Journal (AAM)
In this article Homotopy Perturbation Method (HPM) is applied to obtain an approximate analytical solution of a fractional diffusion equation with an external force and a reaction term different from the reaction term used by Das and Gupta (2010). The anomalous behavior of diffusivity in presence or absence of linear external force due to the presence of this force of reaction term are obtained and presented graphically.