Title of article :
Legendre-collocation spectral solver for variable-order fractional functional differential equations
Author/Authors :
Hafez, Ramy Mahmoud Department of Mathematics - Faculty of Education - Matrouh University, Egypt , Youssri, Youssri Hassan 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 :
Matrix equation , Gauss-Legendre nodes , Shifted Legendre polynomials , Variable-order fractional functional differential equations
Journal title :
Astroparticle Physics
