@article { author = {Erjaee, G. H. and Akrami, M. H. and Atabakzadeh, M. H.}, title = {The operational matrix of fractional integration for shifted Legendre polynomials}, journal = {Iranian Journal of Science}, volume = {37}, number = {4}, pages = {439-444}, year = {2013}, publisher = {Springer}, issn = {2731-8095}, eissn = {2731-8109}, doi = {10.22099/ijsts.2013.1778}, abstract = {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.}, keywords = {Fractional-order differential equation,‎operational matrix,‎shifted Legendre polynomials,‎Riemann-Liouville fractional integral operator}, url = {https://ijsts.shirazu.ac.ir/article_1778.html}, eprint = {https://ijsts.shirazu.ac.ir/article_1778_88564c8b9316dd15c7f33249df8d92e1.pdf} }