TY - JOUR ID - 1778 TI - The operational matrix of fractional integration for shifted Legendre polynomials JO - Iranian Journal of Science JA - ISTT LA - en SN - 2731-8095 AU - Erjaee, G. H. AU - Akrami, M. H. AU - Atabakzadeh, M. H. AD - Department of Mathematics, College of Sciences, Shiraz University, P.O. Box 74811-71466, Shiraz, Iran Y1 - 2013 PY - 2013 VL - 37 IS - 4 SP - 439 EP - 444 KW - Fractional-order differential equation KW - ‎operational matrix KW - ‎shifted Legendre polynomials KW - ‎Riemann-Liouville fractional integral operator DO - 10.22099/ijsts.2013.1778 N2 - In this article we implement an operational matrix of fractional integration for Legendre polynomials. We proposed an algorithm to obtain an approximation solution for fractional differential equations, described in Riemann-Liouville sense, based on shifted Legendre polynomials. This method was applied to solve linear multi-order fractional differential equation with initial conditions, and the exact solutions obtained for some illustrated examples. Numerical results reveal that this method gives ideal approximation for linear multi-order fractional differential equations. UR - https://ijsts.shirazu.ac.ir/article_1778.html L1 - https://ijsts.shirazu.ac.ir/article_1778_88564c8b9316dd15c7f33249df8d92e1.pdf ER -