Fractional-order Bessel wavelet functions for solving variable order fractional optimal control problems with estimation error

Abstract

In the present paper, we apply the fractional-order Bessel wavelets (FBWs) for solving optimal control problems with variable-order (VO) fractional dynamical system. The VO fractional derivative operator is proposed in the sense of Caputo type. To solve the considered problem, the collocation method based on FBWFs, pseudo-operational matrix of VO fractional derivative and the dual operational matrix is proposed. In fact, we convert the problem with unknown coefficients in the constraint equations, performance index and conditions to an optimisation problem, by utilising the proposed method. Also, the convergence of the method with details is discussed. At last, to demonstrate the high precision of the numerical approach, we examine several examples.

Keywords:

• Fracrional-order Bessel wavelet functions
• variable-order fractional pseudo-operational matrix of derivative
• variable-order fractional optimal control problems
• error analysis

Acknowledgments

We express our sincere thanks to the anonymous referees for valuable suggestions that improved the final manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Haniye Dehestani

Haniye Dehestani received his Master's degree in applied mathematics from the Alzahra University in Iran. She then pursued a doctorate at the same university and earned his doctoral degree. She is currently a postdoctoral researcher in the department of mathematics in the Alzahra University.

Yadollah Ordokhani

Yadollah Ordokhani obtained his Masters in applied mathematics from Tarbiat Modares University, Iran in 1987. He received his PhD in applied mathematics from the Amirkabir University of Technology, Iran in 2001. He is currently a professor of applied mathematics in the Alzahra University.

Mohsen Razzaghi

Mohsen Razzaghi received his Bachelor's Degree in Mathematics with a minor in Physics from the University of Sussex in England, and his Master's Degree in Applied Mathematics from the University of Waterloo in Canada. He then returned to Sussex University and earned his doctoral degree. He is currently a professor in the Department of Mathematics and Statistics in the Mississippi State University, and has served as Head of the Department since 2007.