Title of article :
Hybrid Legendre functions to solve differential equations with fractional derivatives
Author/Authors :
Nouri, K Department of Mathematics - Faculty of Mathematics - Statistics and Computer Sciences - Semnan University , Torkzadeh, L Department of Mathematics - Faculty of Mathematics - Statistics and Computer Sciences - Semnan University , Mohammadian, S Department of Mathematics - Faculty of Mathematics - Statistics and Computer Sciences - Semnan University
Abstract :
This paper introduces an approach based on hybrid operational matrix to obtain a numerical scheme to solve fractional
differential equations. The idea is to convert the given equations into a system of equations, based on the block-pulse and
Legendre polynomials. Also, we employ the Banach fixed-point theorem to analyze the problem on the Banach algebra
C[0, b] for some fractional differential equations, which include many key functional differential equations that arise in
linear and nonlinear analysis.
Keywords :
Fractional differential equations , Operational matrix , Legendre polynomials , Block-pulse function , Fixed-point theorem
Journal title :
Astroparticle Physics
