A generalized definition of the fractional derivative with applications
Document Type
Article
Publication Date
10-23-2021
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.
Keywords
Differential-equations, Numerical-solutions, Calculus model
Publication Title
Mathematical Problems in Engineering
Volume
2021
Publisher
Mathematical Problems in Engineering