This paper presents a class of linear and nonlinear delay optimal control problems with mixed control-state constraints using a conformable fractional derivative. We modify the conformable fractional derivative using a novel translation from Caputo-Fabrizio derivative where the kernel is replaced by a suitable exponential function. Using some properties of the modified conformable derivative, fractional dynamic system is first transformed into a non-fractional one. The problem is then transformed to an equivalent problem with a fractional dynamical system without delay, using a Padé approximation. By utilizing the necessary optimality conditions in the form of Pontryagin's minimum principle for the optimal control problems and by constructing an error function, we define an unconstrained minimization problem. An artificial intelligence approach based on a fractional power series neural network scheme for solving the obtained minimization problem is presented. The effectiveness of the proposed idea is illustrated by several numerical examples.