Abstract
This paper discusses the optimal control issue for elliptic k×k cooperative fractional systems. The fractional operators are proposed in the Laplace sense. Because of the nonlocality of the Laplace fractional operators, we reformulate the issue as an extended issue on a semi-infinite cylinder in Rk+1. The weak solution for these fractional systems is then proven to exist and be unique. Moreover, the existence and optimality conditions can be inferred as a consequence.
Subject
Statistics and Probability,Statistical and Nonlinear Physics,Analysis