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

Hafez, Ramy Mahmoud; Youssri, Youssri Hassan

doi:10.22034/cmde.2019.9465

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

10.22034/cmde.2019.9465

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