Solving Fractional-Order Diffusion Equations in a Plasma and Fluids via a Novel Transform

Abstract

Motivated by the importance of diffusion equations in many physical situations in general and in plasma physics in particular, therefore, in this study, we try to find some novel solutions to fractional-order diffusion equations to explain many of the ambiguities about the phenomena in plasma physics and many other fields. In this article, we implement two well-known analytical methods for the solution of diffusion equations. We suggest the modified form of homotopy perturbation method and Adomian decomposition methods using Jafari-Yang transform. Furthermore, illustrative examples are introduced to show the accuracy of the proposed methods. It is observed that the proposed method solution has the desire rate of convergence toward the exact solution. The suggested method’s main advantage is less number of calculations. The proposed methods give series form solution which converges quickly towards the exact solution. To show the reliability of the proposed method, we present some graphical representations of the exact and analytical results, which are in strong agreement with each other. The results we showed through graphs and tables for different fractional-order confirm that the results converge towards exact solution as the fractional-order tends towards integer-order. Moreover, it can solve physical problems having fractional order in different areas of applied sciences. Also, the proposed method helps many plasma physicists in modeling several nonlinear structures such as solitons, shocks, and rogue waves in different plasma systems.