OICC Press International Journal of Mathematical Modelling & Computations 2228-6233 15 4 2025 08 10 Solving fractional optimal control problems and costate estimation via a Muntz pseudospectral method 10.57647/ijm2c.2025.150423 EN Hussein Ghassemi Mohammad Maleki Department of Mathematics, Isf. C. Islamic Azad University, Isfahan, Iran. Journal Article 2025 08 10 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.