Necessary optimality conditions for a Lagrange problem governed by a continuous Roesser model with Caputo derivatives

Abstract

In the paper, we consider a Lagrange problem governed by a continuous Roesser type system with single partial Caputo derivatives. The necessary optimality conditions for such a problem are derived. In our approach, the increment method, as well as a fractional version of Gronwall’s type lemma for functions of two variables are used.

Keywords

• partial fractional integrals and derivatives
• roesser type system
• maximum principle
• lagrange type cost functional