Modified Three-Point Fractional Formulas with Richardson Extrapolation

Iqbal M. Batiha (), Shameseddin Alshorm (), Adel Ouannas, Shaher Momani, Osama Y. Ababneh and Meaad Albdareen
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Iqbal M. Batiha: Department of Mathematics, Faculty of Science and Technology, Irbid National University, Irbid 2600, Jordan
Shameseddin Alshorm: Department of Mathematics, Al Al-Bayt University, Mafraq 25113, Jordan
Adel Ouannas: Department of Mathematics and Computer Science, University of Larbi Ben M’hidi, Oum El Bouaghi 04000, Algeria
Shaher Momani: Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman 346, United Arab Emirates
Osama Y. Ababneh: Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, Jordan
Meaad Albdareen: Department of Mathematics, Al Al-Bayt University, Mafraq 25113, Jordan

Mathematics, 2022, vol. 10, issue 19, 1-16

Abstract: In this paper, we introduce new three-point fractional formulas which represent three generalizations for the well-known classical three-point formulas; central, forward and backward formulas. This has enabled us to study the function’s behavior according to different fractional-order values of α numerically. Accordingly, we then introduce a new methodology for Richardson extrapolation depending on the fractional central formula in order to obtain a high accuracy for the gained approximations. We compare the efficiency of the proposed methods by using tables and figures to show their reliability.

Keywords: Richardson extrapolation; Riemann–Liouville fractional derivative and integral; Lagrange interpolating polynomial; Caputo derivative (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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