On convergence analysis and numerical solutions of local fractional Helmholtz equation

Abstract

Local fractional q-homotopy analysis transform method (q-HATM) is employed to solve the local fractional Helmholtz equation. Uniqueness and convergence analysis of the method is investigated by Banach's fixed point theory. Solutions are expressed in the form of rapidly series with fast computable basics by Mathematica software. Reliability analysis is provided. Computational results display that LFq-HATM is an efficient and powerful method to obtain solutions to the present equation and has the potential to be applicable to other related fractional-order systems. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University.