Vol. 6(2). July 2015, No. 6, pp. 53-64.

NUMERICAL AND THEORETICAL STUDY FOR SOLVING MULTI-TERM LINEAR FRACTIONAL DIFFERENTIAL EQUATIONS USING A COLLOCATION METHOD BASED ON THE GENERALIZED LAGUERRE POLYNOMIALS
Vol. 6 (2). July 2015, No. 6, pp. 53-64
M. M. KHADER, N. H. SWEILAM

Abstract

Abstract. In this paper, a direct solution technique for solving multi-order linear fractional differential equations (LFDEs) with variable coefficients is developed using a collocation method based on the generalized Laguerre polynomials. Taking the advantages of the Laguerre polynomials, to introduce an approximate formula of the derivatives of any fractional order. The fractional derivatives are presented in terms of the Caputo sense. Special attention is given to study the convergence analysis and estimate an upper bound of the error of the proposed formula. The properties of Laguerre polynomials are utilized to reduce LFDEs to a system of algebraic equations which can be solved using an efficient numerical method. Several numerical examples are provided to confirm the theoretical results and the efficiency of the proposed method.


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