A homotopy based computational scheme for local fractional Helmholtz and Laplace equations

Jagdev Singh; Ritin Babu; Ved Prakash Dubey; Devendra Kumar

A homotopy based computational scheme for local fractional Helmholtz and Laplace equations

Authors

Jagdev Singh Department of Mathematics, JECRC University, Jaipur-303905, Rajasthan, India https://orcid.org/0009-0005-3174-762X
Ritin Babu Department of Mathematics, JECRC University, Jaipur-303905, Rajasthan, India https://orcid.org/0009-0005-3174-762X
Ved Prakash Dubey Faculty of Mathematical and Statistical Sciences, Shri Ramswaroop Memorial University, Barabanki-225003, Uttar Pradesh, India https://orcid.org/0009-0005-3174-762X
Devendra Kumar Department of Mathematics, University of Rajasthan, Jaipur-302004, Rajasthan, India https://orcid.org/0009-0005-3174-762X

Keywords:

Local fractional derivative operator; Partial differential equations; Laplace equation; Helmholtz equation; q-local fractional homotopy analysis transform method

Abstract

In this work, we investigate solutions for the local fractional Helmholtz and Laplace equations on Cantor set having importance in electrostatics, gravitation and fluid dynamics. To find exact solutions, the q-local fractional homotopy analysis transform method (q-LFHATM) has been used. The numerical results computed with the aid of the applied scheme shows that it is an efficient and accurate tool to solve differential equations with local fractional derivatives

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Published

2023-09-18

How to Cite

Jagdev Singh, Ritin Babu, Ved Prakash Dubey, & Devendra Kumar. (2023). A homotopy based computational scheme for local fractional Helmholtz and Laplace equations. Journal of Computational Analysis and Applications (JoCAAA), 31(3), 444–457. Retrieved from https://www.eudoxuspress.com/index.php/pub/article/view/91