Theses and Dissertations

ORCID

https://orcid.org/0000-0003-4019-1756

Issuing Body

Mississippi State University

Advisor

Razzaghi, Mohsen

Committee Member

Dang, Hai

Committee Member

Kim, Seongjai

Committee Member

Qian, Chuanxi

Committee Member

Sepehrifar, Mohammad

Date of Degree

5-13-2022

Document Type

Dissertation - Open Access

Major

Mathematics

Degree Name

Doctor of Philosophy (Ph.D)

College

College of Arts and Sciences

Department

Department of Mathematics and Statistics

Abstract

This thesis presents a numerical approach based on generalized fractional-order Chebyshev wavelets for solving fractional-order optimal control problems. The exact value of the Riemann– Liouville fractional integral operator of the generalized fractional-order Chebyshev wavelets is computed by applying the regularized beta function. We apply the given wavelets, the exact formula, and the collocation method to transform the studied problem into a new optimization problem. The convergence analysis of the proposed method is provided. The present method is extended for solving fractional-order, distributed-order, and variable-order optimal control problems. Illustrative examples are considered to show the advantage of this method in comparison with the existing methods in the literature.

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