Mississippi State University
Date of Degree
Dissertation - Open Access
Doctor of Philosophy (Ph.D)
College of Arts and Sciences
Department of Mathematics and Statistics
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.
Ghanbari, Ghodsieh, "A novel Chebyshev wavelet method for solving fractional-order optimal control problems" (2022). Theses and Dissertations. 5475.