Alexandria Engineering Journal

Alexandria Engineering Journal

Volume 59, Issue 6, December 2020, Pages 4335-4341
Alexandria Engineering Journal

On convergence analysis and numerical solutions of local fractional Helmholtz equation

https://doi.org/10.1016/j.aej.2020.07.038Get rights and content
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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.

Keywords

q-HATM
Local fractional Helmholtz equation
Banach’s fixed point theory
Laplace transform

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Peer review under responsibility of Faculty of Engineering, Alexandria University.

© 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University.