Chapter 15 - Weak Pontryagin's maximum principle for optimal control problems involving a general analytic kernel

Abstract

We prove a duality relation and an integration-by-parts formula for fractional operators with a general analytical kernel. Based on these basic results, we are able to prove a new Grönwall inequality and continuity and differentiability of solutions of control differential equations. This allows us to obtain a weak version of Pontryagin's maximum principle. Moreover, our approach allow us to consider mixed problems with both integer- and fractional-order operators and derive necessary optimality conditions for isoperimetric variational problems and other problems of the calculus of variations.