AUTHOR(S): Fatma Ayaz, Onur Gorgulu

TITLE A Hybrid Method for Solving Some Particular Types of Fractional Differential Equations 
KEYWORDS Fractional Order Differential Equations, Hadamard Finite Part Integral and Finite Difference Method: Typing manuscripts, LATEX 
ABSTRACT This paper investigates the numerical solution of some particular types of fractional order differential equations which involve multi derivative terms. Fractional equations have advantages when compared with the integer order ones, since they describe some natural physical processes and dynamical systems much better. There are some suggested numerical algorithms for these types of equations but they usually involve a single term. Therefore, we present a hybrid method here. According to the method, the fractional order derivative is written in terms of Riemann Liouville integral and this integral is evaluated as Hadamard finitepart integral numerically as in [1]. On the other hand, the other ordinary derivatives are discretized in terms of standard finite difference approximation. In this study, error estimate has been dealt with and reliability and convergency of the method are tested on some illustrative examples. 
Cite this paper Fatma Ayaz, Onur Gorgulu. (2017) A Hybrid Method for Solving Some Particular Types of Fractional Differential Equations. International Journal of Mathematical and Computational Methods, 2, 15 