Numerical approach of riemann-liouville fractional derivative operator

Ramzi B. Albadarneh (The Hashemite University)
Iqbal M. Batiha (Irbid National University,)
Ahmad Adwai (The Hashemite University)
Nedal Tahat (The Hashemite University)
A. K. Alomari (Yarmouk University)

International Journal of Electrical and Computer Engineering
Vol 11, No 6: December 2021

This article introduces some new straightforward and yet powerful formulas in the form of series solutions together with their residual errors for approximating the Riemann-Liouville fractional derivative operator. These formulas are derived by utilizing some of forthright computations, and by utilizing the so-called weighted mean value theorem (WMVT). Undoubtedly, such formulas will be extremely useful in establishing new approaches for several solutions of both linear and nonlinear fractionalorder differential equations. This assertion is confirmed by addressing several linear and nonlinear problems that illustrate the effectiveness and the practicability of the gained findings.