Article
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On Gohar Fractional Calculus
Version 1
: Received: 24 February 2024 / Approved: 26 February 2024 / Online: 29 February 2024 (09:13:33 CET)
How to cite: Gohar, A.; Younes, M.; Doma, S. On Gohar Fractional Calculus. Preprints 2024, 2024021667. https://doi.org/10.20944/preprints202402.1667.v1 Gohar, A.; Younes, M.; Doma, S. On Gohar Fractional Calculus. Preprints 2024, 2024021667. https://doi.org/10.20944/preprints202402.1667.v1
Abstract
Recently, Gohar et al. introduced a novel, local, and well-behaved fractional calculus. It possesses all the classical properties, and Its locality imposes simplicity and accuracy in modeling fractional order systems. In this article, we further develop the definitions and extend the classical properties of Gohar fractional calculus to address some of the open problems in Calculus. The fractional Gronwall's integral inequality, Taylor power series expansion, and Laplace transform are defined and applied to overcome some of the limitations in the classical integer-order calculus. The fractional Laplace transform is applied to solve Bernoulli-type logistic and Bertalanffy nonlinear fractional differential equations, and the criteria under which it can be applied to solve linear differential equations are investigated.
Keywords
Gohar fractional calculus; Gohar fractional Laplace transform; Gohar fractional power series expansion; Left and right Gohar fractional derivatives; Left and right Gohar fractional integrals
Subject
Computer Science and Mathematics, Mathematics
Copyright: 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.
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