Mississippi State University
Miller, T. Len
Date of Degree
Dissertation - Open Access
Doctor of Philosophy
College of Arts and Sciences
Department of Mathematics and Statistics
In this dissertation, a new numerical method for solving fractional calculus problems is presented. The method is based upon the fractional Taylor vector approximations. The operational matrix of the fractional integration for the fractional Taylor vector is introduced. This matrix is then utilized to reduce the solution of the fractional calculus problems to the solution of a system of algebraic equations. This method is used to solve fractional differential equations, Bagley-Torvik equations, fractional integro-differential equations, and fractional duffing problems. Illustrative examples are included to demonstrate the validity and applicability of this technique.
KrishnasamySaraswathy, Vidhya, "The Numerical Solutions of Fractional Differential Equations with Fractional Taylor Vector" (2016). Theses and Dissertations. 4576.