Chapter 15: Weak Pontryagin's maximum principle for optimal control problems involving a general analytic kernel☆
Faïçal Ndaïrou; Delfim F.M. Torres Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, Aveiro, Portugal
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 ...
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