Numerical solutions for fractional optimal control problems by using generalised fractional-order Chebyshev wavelets

Abstract

This paper proposes a new numerical method for solving fractional optimal control problems (FOCPs). The method is based on generalised fractional-order Chebyshev wavelets (GFOCW). The exact value of the Riemann–Liouville fractional integral operator of the GFOCW is given by applying the incomplete beta function. By using the properties of GFOCW and the collocation method, the FOCP is reduced to a parameter optimisation problem. The last problem is solved by known algorithms. Six numerical examples are given. One of them is an application example in a cancer model. Through these numerical examples, we will show that for some cases of our examples, we will get the exact solutions. These solutions were not obtained previously in the literature. In addition, our method gives more accurate results in comparison with the existing methods.