Open AccessNumerical approach of riemann-liouville fractional derivative operator
Author(s) -
Ramzi B. Albadarneh,
Iqbal M. Batiha,
Ahmad Adwai,
Nedal Tahat,
A. K. Alomari
Publication year - 2021
Publication title -
international journal of power electronics and drive systems/international journal of electrical and computer engineering
Language(s) - English
Resource type - Journals
eISSN - 2722-2578
pISSN - 2722-256X
DOI - 10.11591/ijece.v11i6.pp5367-5378
Subject(s) - fractional calculus , assertion , mathematics , differential operator , operator (biology) , nonlinear system , derivative (finance) , residual , computation , algebra over a field , mathematical analysis , calculus (dental) , pure mathematics , computer science , algorithm , physics , medicine , biochemistry , chemistry , dentistry , repressor , quantum mechanics , transcription factor , financial economics , economics , gene , programming language
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.