Mojtaba Rasouli Gandomani, M. Tavassoli Kajani
Department of Mathematics
Isfahan (Khorasgan) Branch
Islamic Azad University
Isfahan, IRAN

Abstract. In this paper, the technique of the interval division based on the shifted Müntz-Legendre polynomials is used to present an approximate solution for the fractional differential equations. The first step of proposed method is to divide the interval which is considered for the solution into several subintervals with a specific step size. We obtain an approximate solution of the problem on each of subintervals using the collocation method and the shifted Müntz-Legendre polynomials. The use of the shifted Müntz- Legendre polynomials and the technique of the interval division simultaneously lead to more accuracy. The accuracy and convergence of the method are demonstrated with several numerical examples.

Received: April 20, 2015

AMS Subject Classification: 34K28, 65R99, 65L99

Key Words and Phrases: shifted Müntz-Legendre polynomials, fractional differential equations, approximate solution, collocation method

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