Existence and discrete approximation for optimization problems governed by fractional differential equations

We investigate a class of generalized differential optimization problems driven by the Caputo derivative. Existence of weak Carathe´odory solution is proved by using Weierstrass existence theorem, fixed point theorem and Filippov implicit function lemma etc. Then a numerical approximation algorithm is introduced, and a convergence theorem is established. Finally, a nonlinear programming problem constrained by the fractional differential equation is illustrated and the results verify the validity of the algorithm.