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 solutions 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 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
