Analytical approximate solutions of some fractional nonlinear evolution equations through AFVI method

• Formulate of a novel, suitable and effective alternative fractional variational iteration method (AFVI method). • Involve the Caputo fractional order derivative to fractionalize some physically important nonlinear evolution equations (NLEEs). • Analyze the convergence of the proposed AFVI method. • Determine a new series of analytical approximate solutions (AASs) for the considered fractional NLEEs (FNLEEs) applying AFVI method. • Demonstrate the graphical and numerical comparisons among the newly obtain AASs, exact solutions and other existing analogous AASs of the considered FNLEEs. In this article, we construct and investigate a new fractional variational iteration technique which is named as AFVI method. After that, we formulate some IVPs corresponding to the fractional nonlinear evolution equations NLTFFWE, mNLTFFWE, TFmCHE and TFmDPE. The Caputo fractional order derivative has been used to fractionalize the considered NLEEs. Then, we solve the considered IVPs by applying the formulated AFVI method. Lastly, we check the accuracy of the attained AASs by making some graphical and numerical comparisons with their corresponding exact solutions and other existing equivalent AASs. The result of this article confirm that the efficiency, appropriateness and time spent capability of the newly constructed AFVI method are better than that of the other existing analogous fractional analytical approximation methods. Here, we apply the Maple 2021 programming software to obtain the AASs of the formulated IVPs and drawing the 3D graphs of the attained AASs. Finally, in this article we validate the applicability of the Caputo fractional order derivative to form a novel analytical approximation method as well as to fractionalize some essential NLEEs of Mathematical physics.