Theses and Dissertations

Issuing Body

Mississippi State University


Razzaghi, Mohsen

Committee Member

Qian, Chuanxi

Committee Member

Kim, Seongjai

Committee Member

Yarahmadian, Shantia

Committee Member

Miller, T. Len

Date of Degree


Document Type

Dissertation - Open Access

Degree Name

Doctor of Philosophy


College of Arts and Sciences


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.