Optimal semi-analytical solutions of time-fractional evolution equations

This study focuses on the optimal semi-analytical solutions of time-fractional evolution equations. First of all, the classical evolution equations are converted to time-fractional evolution equations using Caputo-Fabrizio fractional derivative. The advantage of Caputo-Fabrizio fractional derivative is that its kernel is non-singular and because of that, there is no complexity in the implementation of Caputo-Fabrizio fractional derivative. Then, the time-fractional evolution equations are solved using a semi-analytical technique, which is the combination of Laplace transform and Picard's iterative scheme. The derived solutions are innovative, and previous literature lacks such derivations. In addition, the stability analysis of implemented semi-analytical technique is also carried out by using Banach contraction principle and g-stable mapping. Moreover, the efficacy of Caputo-Fabrizio fractional derivative is exhibited through graphical illustrations, and numerical results are drafted in tabular form for specific values of fractional parameter to further validate the efficiency of implemented semi-analytical technique for time-fractional evolution equations.