Abstract
In the present note, a new modification of the Adomian decomposition method is developed for the solution of fractional-order diffusion-wave equations with initial and boundary value Problems. The derivatives are described in the Caputo sense. The generalized formulation of the present technique is discussed to provide an easy way of understanding. In this context, some numerical examples of fractional-order diffusion-wave equations are solved by the suggested technique. It is investigated that the solution of fractional-order diffusion-wave equations can easily be handled by using the present technique. Moreover, a graphical representation was made for the solution of three illustrative examples. The solution-graphs are presented for integer and fractional order problems. It was found that the derived and exact results are in good agreement of integer-order problems. The convergence of fractional-order solution is the focus point of the present research work. The discussed technique is considered to be the best tool for the solution of fractional-order initial-boundary value problems in science and engineering.
Highlights
IntroductionPublisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations
We will present the solution of some illustrative examples by using the new technique based on Adomian decomposition method (ADM)
Three examples of fractional-order diffusion-wave equations (FDWEs) are presented to confirm the validity of the suggested method
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. The fractional-diffusion equations (FDEs) were introduced by Nigmatullin [34] in physics to describe the special type of porous media He discovered that some of the electromagnetic, mechanical and acoustic can be modeled more properly with the help of FDWEs. The FDEs are solved by Mark M. We will use a new technique of ADM for the solution of FDWEs along with initial and boundary conditions, as used by Elaf Jaafer Ali in [65]. He applied the same procedure for the fourth order parabolic PDEs in combination with variation iteration method in [66,67].
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