A generalized definition of the fractional derivative with applications

Abu-Shady, M. and Kaabar, Mohammed K. A. (2021) A generalized definition of the fractional derivative with applications. Mathematical Problems in Engineering, 2021. ISSN 1024-123X, DOI https://doi.org/10.1155/2021/9444803.

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A generalized fractional derivative (GFD) definition is proposed in this work Fora differentiable function expanded by a Taylor series, we show that (DD beta)-D-alpha f (t) = D alpha+beta f (t); 0 < alpha <= 1; 0 < beta <= 1. GFD is applied for some functions to investigate that the GFD coincides with the results from Caputo and Riemann-Liouville fractional derivatives. The solutions of the Riccati fractional differential equation are obtained via the GFD. A comparison with the Bernstein polynomial method (BPM), enhanced homotopy perturbation method (EHPM), and conformable derivative (Cl)) is also discus sal. Our results show that the proposed definition gives a much better accuracy than the wellknown definition of the conformable derivative. Therefore, GFD has advantages in comparison with other related definitions. This work provides a new path for a simple tool for obtaining analytical solutions of many problems in the context of fractional calculus.

Item Type: Article
Uncontrolled Keywords: Differential-equations;Numerical-solutions;Calculus model
Subjects: Q Science > QA Mathematics
Depositing User: Ms Zaharah Ramly
Date Deposited: 27 Oct 2022 06:14
Last Modified: 27 Oct 2022 06:14
URI: http://eprints.um.edu.my/id/eprint/35329

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