Open Journal of Mathematical Analysis
Vol. 7 (2023), Issue 1, pp. 01 – 09
ISSN: 2616-8111 (Online) 2616-8103 (Print)
DOI: 10.30538/psrp-oma2023.0119
The local fractional natural transform and its applications
to differential equations on Cantor sets
Djelloul Ziane\(^{1,*}\), and Mountassir Hamdi Cherif\(^{2}\)
\(^{1}\) Department of Mathematics, Faculty of Mathematics and Material Sciences, Kasdi Merbah University of Ouargla,
Algeria
\(^{2}\) Hight School of Electrical and Energetics Engineering of Oran (ESGEE-Oran), Oran, Algeria
Copyright © 2023 Djelloul Ziane, and Mountassir Hamdi Cherif. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received: May 06, 2023 – Accepted: June 20, 2023 – Published: June 30, 2023
Abstract
The work that we have done in this paper is the coupling method between the local fractional derivative and the Natural transform (we can call it the local fractional Natural transform), where we have provided some essential results and properties. We have applied this method to some linear local fractional differential equations on Cantor sets to get nondifferentiable solutions. The results show this transform’s effectiveness when we combine it with this operator.
Keywords:
local fractional calculus; local fractional Laplace transform; natural transform method; local fractional differential equations.