Mississippi State University
Johnson, Corlis P.
Other Advisors or Committee Members
Miller, T. Len
Date of Degree
Dissertation - Open Access
Doctor of Philosophy (Ph.D)
College of Arts and Sciences
Department of Mathematics and Statistics
In this dissertation, a new numerical method for solving the fractional dynamical systems, is presented. We first introduce Riemann-Liouville fractional integral operator for hybrid functions. Then we will show the spectral accuracy of the present method for solving fractional-order differential equations, and we will extend the present method for solving nonlinear fractional integro-differential equations, fractional Bagley-Torvik equation, distributed order fractional differential equations, two-dimensional fractional partial differential equations, and fractional optimal control problems. In all cases, we will show the rate of convergence is more than some existing numerical methods which were used to solve these kind of problems in the literature. Illustrative examples are included to demonstrate the validity and applicability of the technique.
Mashayekhi, Somayeh, "Hybrid functions in Fractional Calculus" (2015). Theses and Dissertations. 2523.