Hybrid of block-pulse functions and generalized Mott polynomials and their applications in solving delay fractional optimal control problems

We give the hybrid of block-pulse function and generalized Mott polynomials (HBGMP) and use it to solve delay fractional optimal control problems (DFOCPs). First, we develop a method for computing the exact formula of the Riemann-Liouville fractional integral operator of the HBGMP by using the regularized beta function. Next, the DFOCPs will be transformed into parameter optimization problems. By imposing the optimality conditions, we reduce the problem to algebraic equations. Several examples are given to show the advantages of the method.