Global optimization of a nonlinear system of differential equations involving \(\psi \)-Hilfer fractional derivatives of complex order

In this paper, a class of cyclic (noncyclic) operators of condensing nature are defined on Banach spaces via a pair of shifting distance functions. The best proximity point (pair) results are manifested using the concept of measure of noncompactness (MNC) for the said operators. The obtained best proximity point result is used to demonstrate existence of optimum solutions of a system of differential equations involving \(\psi \) $\psi$ -Hilfer fractional derivatives of complex order.