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

Document Type : Research Paper

Authors

1 Department of Mathematics, Faculty of Education, Matrouh University, Egypt.

2 Department of Mathematics, Faculty of Science, Cairo University, Giza-Egypt

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.

Keywords


Volume 8, Issue 1
January 2020
Pages 99-110
  • Receive Date: 24 May 2018
  • Revise Date: 11 March 2019
  • Accept Date: 07 April 2019
  • First Publish Date: 01 January 2020