In this work, we study the existence of optimal solutions of a system of differential equations involving the \((j, \varphi )\) -Hilfer fractional derivative. This goal is achieved by means of the existence of best proximity point for the cyclic operator defined from the system of fractional differential equations. In addition, we prove the new best proximity point (pair) results for novel classes of cyclic (noncyclic) mappings. The concept of measure of noncompactness is used to derive the results which make it more general.