Robust Approach for Uncertain Multi-Dimensional Fractional Control Optimization Problems

In this paper, we focus our study on a multi-dimensional fractional control optimization problem involving data uncertainty (FP) and derive the parametric robust necessary optimality conditions and its sufficiency by imposing the convexity hypotheses on the involved functionals. We also construct the parametric robust dual problem associated with the above-considered problem (FP) and establish the weak and strong robust duality theorems. The strong robust duality theorem asserts that the duality gap is zero under the convexity notion. In addition, we formulate some examples to validate the stated conclusions.