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In this article, a class of cyclic (noncyclic) operators are defined on Banach spaces via concept of measure of noncompactness using some abstract functions. The best proximity point (pair) results are manifested for the said operators. The obtained main results are applied to demonstrate the existence of optimum solutions of a system of fractional differential equations involving(k,ψ)\left(k,\psi )-Hilfer fractional derivatives.

Global optimum solutions for a system of ( k , ψ )-Hilfer fractional differential equations: Best proximity point approach