Abstract
In this article, we also introduced two well-known computational techniques for solving the time-fractional Fornberg–Whitham equations. The methods suggested are the modified form of the variational iteration and Adomian decomposition techniques by ρ-Laplace. Furthermore, an illustrative scheme is introduced to verify the accuracy of the available methods. The graphical representation of the exact and derived results is presented to show the suggested approaches reliability. The comparative solution analysis via graphs also represented the higher reliability and accuracy of the current techniques.
Highlights
With engineering and science development, non-linear evolution models have been analyzed as the problems to define physical phenomena in plasma waves, fluid mechanics, chemical physics, solid-state physics, etc
We suggested a new iterative technique with ρ-Laplace transformation to investigate fractional-order ordinary and partial differential equations with fractional-order Caputo derivative
It is investigated that the results achieved in the series form have a higher convergence rate towards the exact results
Summary
With engineering and science development, non-linear evolution models have been analyzed as the problems to define physical phenomena in plasma waves, fluid mechanics, chemical physics, solid-state physics, etc. Compared to Adomian’s decomposition process, VITM solves the problem without the need to compute Adomian’s polynomials This scheme provides a quick result to the equation, whereas the [29] mesh point techniques provide an analytical solution. An American mathematician, developed the Adomian decomposition technique It focuses on finding series-like results and decomposing the non-linear operator into a sequence, with the terms presently computed using Adomian polynomials [30]. This method is modified with ρ-Laplace transform, so the modified approach is the ρ-Laplace decomposition method. The ρ-LDM and ρ-LVIM achieve the approximate results in the form of series results
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