On a new variant of cyclic (noncyclic) condensing operators with existence of optimal solutions to an FDE

The paper is designed to highlight the presence of an optimal solution to a differential system comprising fractional order derivatives, precisely the ψ-Caputo derivative, under the prescribed initial constraints. This is attained through a new variant of cyclic (noncyclic) condensing operators incorporating a pair of maps. The altered notion facilitates in evolving best proximity point (pair) results as well as coupled best proximity point results with supportive corollaries.