2025/08/10 by Ghassemi, Hussein, Maleki, Mohammad
#Costate estimation #Fractional cancer model #Fractional optimal control #M¨untz polynomials #Pseudospectral
paper · doi:10.57647/ijm2c.2025.150423
In this paper, we first introduce the Muntz–Legendre polynomials and establish their relation to Jacobi polynomials. Then, a stable scheme is presented for approximating the Caputo fractional derivative of the Muntz–Legendre polynomials. Next, we introduce a Muntz–polynomial pseudospectral method with fractional power of Legendre–Gauss– Radau mesh points for solving fractional optimal control problems. This method is particularly suitable for problems whose solutions contain non-integer exponent factors. We also construct a novel costate estimation procedure based on the first order optimality conditions and the structure of the underlying problem. Three numerical examples, including a fractional model for tumor burden under immune suppression, are presented to demonstrate the applicability and spectral accuracy of the proposed method.