A collocation method for solving the fractional calculus of variation problems

Mohammad Reza Ahmadi; Mitra Nasiri

doi:10.5269/bspm.v35i1.26333

Mohammad Reza Ahmadi Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahrekord University , P. O. Box. 115, Shahrekord, Iran
Mitra Nasiri Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahrekord University , P. O. Box. 115, Shahrekord, Iran

DOI: https://doi.org/10.5269/bspm.v35i1.26333

Keywords: Muntz-Legendre polynomials, orthogonal system, fractional dierential equation, collocation method, Capotu fractional derivative

Abstract

In this paper we use a family of Muntz polynomials and a computational technique based on the collocation method to solve the calculus variation problem. This approach is utilized
to reduce the solution of linear and nonlinear fractional order dierential equations to the solution of a system of algebraic equations. Thus we can obtain a good approximation even
by using a smaller of collocation points.

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