Shifted fractional Jacobi collocation method for solving fractional functional differential equations of variable order

M.A. Abdelkawy, António M. Lopes and Mohammed M. Babatin

Chaos, Solitons & Fractals, 2020, vol. 134, issue C

Abstract: Functional differential equations have been widely used for modeling real-world phenomena in distinct areas of science. However, classical calculus can not provide always the best description of some complex phenomena, namely those observed in biological systems and medicine. This paper proposes a new numerical method for solving variable order fractional functional differential equations (VO-FFDE). Firstly, the shifted fractional Jacobi collocation method (SF-JC) is applied to solve the VO-FFDE with initial conditions. Then, the SF-JC is applied to the VO-FFDE with boundary conditions. Several numerical examples with different types of VO-FFDE demonstrate the superiority of the proposed method.

Keywords: Collocation method; Shifted fractional Jacobi-Gauss-Lobatto quadrature; Shifted fractional Jacobi-Gauss-Radau quadrature; Functional differential equation; Caputo fractional derivative (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:134:y:2020:i:c:s0960077920301235

DOI: 10.1016/j.chaos.2020.109721

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