Application of reproducing kernel Hilbert space method to some ordinary Differential equations of fractional order

Abstract

In this thesis, based on the reproducing kernel Hilbert space method (RKHSM) an e cient algorithm is presented for solving ordinary di erential equations of frac- tional order. We applied RKHSM to obtain pproximate solution for a general form of rst and second order fractional di erential equations. The analytical and ap- proximate solutions are represented in the form of series in the reproducing kernel space W m 2 [a; b]. The n􀀀term approximation and all its derivatives are obtained and proved to converge uniformly to the analytical solution and all its derivatives, re- spectively. The proposed method has an advantage that it is possible to pick any point in the interval of integration. Numerical examples are given to demonstrate the computation e ciency of the presented method. The results of applying this method to the studied cases show the high accuracy, simplicity and e ciency of the approach.