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.
Full text not available from this repository.Abstract
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 |
|---|---|
| Funders: | UNSPECIFIED |
| 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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