A Numerical Approach for Dealing with Fractional Boundary Value Problems

Abeer A. Al-Nana (), Iqbal M. Batiha and Shaher Momani
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Abeer A. Al-Nana: Department of Mathematics, Prince Sattam Bin Abdulaziz University, Alkharj 11942, Saudi Arabia
Iqbal M. Batiha: Department of Mathematics, Al Zaytoonah University of Jordan, Amman 11733, Jordan
Shaher Momani: Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman 346, United Arab Emirates

Mathematics, 2023, vol. 11, issue 19, 1-12

Abstract: This paper proposes a novel numerical approach for handling fractional boundary value problems. Such an approach is established on the basis of two numerical formulas; the fractional central formula for approximating the Caputo differentiator of order α and the fractional central formula for approximating the Caputo differentiator of order 2 α , where 0 < α ≤ 1 . The first formula is recalled here, whereas the second one is derived based on the generalized Taylor theorem. The stability of the proposed approach is investigated in view of some formulated results. In addition, several numerical examples are included to illustrate the efficiency and applicability of our approach.

Keywords: fractional boundary value problem; fractional central formulas; Caputo differentiator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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