An efficient homotopy permutation technique for solving fractional differential equations using Atangana-Baleanu-Caputo operator

This paper discusses the natural homotopy permutation method (NHPM) for solving fractional differential equations (FDEs) with the Atangana-Baleanu-Caputo operator (ABCO) in terms of its derivation, its convergence analysis, and the solution of some DEs using it. Some basic definitions were mentioned to understand the idea and the analysis of the method was presented in addition to three theorems with their proof to prove the convergence of that method, and in the end, the method was applied to solve the Burger's equation and a non-linear system and the method effective.