Numerical approach on time-fractional Sawada-Kotera equation based on fuzzy extension of generalized dual parametric homotopy algorithm

Abstract

This paper develops a fuzzy non-linear fifth-order time-fractional Sawada-Kotera model with a singular kernel and a non-singular Mittag-Leffler kernel. The proposed fractional differential equation is discussed with the Caputo and ABC fractional derivative under strongly generalized results and with fuzzy modelling. A novel double parametric scheme, i.e., q-homotopy analysis generalized transform approach (q-HAGTM), is considered to find the solution of the proposed model with Caputo and ABC fractional derivatives. The problem’s uniqueness and convergence analysis are investigated using Banach’s fixed point theorem. Finally, the numerical results are validated by comparing them with the available results in Caputo and ABC sense under strongly generalized derivatives in the crisp case.