SOLUTION OF SOME TYPES FOR MULTI-FRACTIONAL ORDER DIFFERENTIAL EQUATIONS CORRESPONDING TO OPTIMAL CONTROL PROBLEMS

Abstract

This paper introduces a Multi-Order Fractional Optimal Control Problems in which the dynamic system involves integer and fractional-order derivatives are introduced in the Caputo sense. We derive the necessary optimality conditions in terms of the associated Hamiltonian, and we construct an approximation of the right Riemann−Liouville fractional derivatives and solve the fractional boundary value problems by the spectral method. Numerical methods rely on the spectral method where Chebyshev polynomials are used to approximate the unknown functions. Chebyshev polynomials are widely used in numerical computation to solve the problems are presented.