Analyzing the influence of fractional orders of FitzHugh-Nagumo and Fisher equations

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In this paper, we have applied two semi-analytical techniques: the Mohand variational iteration method (MVIM) and the q-homotopy Mohand transform method (q-HMTM) to derive approximate solutions of fractional-order nonlinear partial differential equations. Particularly, time-fractional FitzHugh Nagumo equation and Fisher equation based on Caputo derivative are explored. Both of them utilize well the features of Mohand transform and fractional calculus to represent the nonlocal and memory-dependent nature of the models. The validity and reliability of the suggested methods are justified by the comparison of the obtained solutions with the exact solutions known in the integer-order limit. The graphical and tabular analysis shows how the fractional order parameter ψ has a great impact on the solution profiles, and a smoothing effect and a delaying propagation effect occur as the fractional order parameter ψ reduces. In a close comparative analysis, both q-HMTM and MVIM provide highly precise results, where MVIM in some instances has a little better accuracy. The results affirm the effectiveness of these methods in addressing new complex systems of a fractional-order that occur in biological, physical, and engineering scenarios.