Legendre-collocation spectral solver for variable-order fractional functional differential equations

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Hafez Ramy Mahmoud; YOUSSRI YOUSSRI HASSAN

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Journal Paper

Paper Information

Journal: Computational Methods for Differential Equations Year:2020 | Volume:8 | Issue:1 Page(s): 99-110

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Information Journal Paper

Title

Legendre-collocation spectral solver for variable-order fractional functional differential equations

Author(s)

Hafez Ramy Mahmoud | YOUSSRI YOUSSRI HASSAN | Issue Writer Certificate

Keywords

Variable-order fractional functional differential equations

Shifted Legendre polynomials

Gauss-Legendre nodes

Matrix equation

Abstract

A numerical method for the Variable-order fractional functional differential equations (VO-FFDEs) has been developed. This method is based on approximation with Shifted Legendre polynomials. The properties of the latter were stated, first. These properties, together with the shifted Gauss-Legendre nodes were then utilized to reduce the VO-FFDEs into a solution of Matrix equation. Sequentially, the error estimation of the proposed method was investigated. The validity and efficiency of our method were examined and verified via numerical examples.

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APA: Copy

Hafez, Ramy Mahmoud, & YOUSSRI, YOUSSRI HASSAN. (2020). Legendre-collocation spectral solver for variable-order fractional functional differential equations. COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS, 8(1), 99-110. SID. https://sid.ir/paper/345759/en

Vancouver: Copy

Hafez Ramy Mahmoud, YOUSSRI YOUSSRI HASSAN. Legendre-collocation spectral solver for variable-order fractional functional differential equations. COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS[Internet]. 2020;8(1):99-110. Available from: https://sid.ir/paper/345759/en

IEEE: Copy

Ramy Mahmoud Hafez, and YOUSSRI HASSAN YOUSSRI, “Legendre-collocation spectral solver for variable-order fractional functional differential equations,” COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS, vol. 8, no. 1, pp. 99–110, 2020, [Online]. Available: https://sid.ir/paper/345759/en

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