SPLINE SOLUTIONS OF LINEAR FRACTIONAL BVPS WITH TWO CAPUTOS APPROACHES

H. TARIQ1, G. AKRAM2

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Abstract

In this paper, an ecient numerical methods based on cubic polynomial spline func- tions are proposed for the linear fractional boundary value problems (FBVPs) with Caputos left and right fractional operator. In computing the approximation to the solutions of FBVPs, consistency relations have been derived with the help of spline functions. For convergence analysis of this method, it is assumed that the exact solu- tion of FBVP belongs to a class of C6-functions. Numerical examples are considered to illustrate the accuracy and eciency of this method and compare the results with other methods developed by Akram and Tariq in [18] and Zahra and Elkholy in [28-30].

Keywords

Linear FBVPs, Cubic Spline Function, Caputos Fractional Operators, Error Bound.