New best proximity point (pair) theorems via MNC and application to the existence of optimum solutions for a system of ψ-Hilfer fractional differential equations

With the aim to prove the existence of optimum solutions of a system of ψ -Hilfer fractional differential equations, this work considers a new class of cyclic (noncyclic) condensing operators in Banach spaces. The best proximity point (pair) results are manifested using the concept of measure of noncompactness for the said operators. The obtained best proximity point results are used to demonstrate existence of optimum solutions of a system of differential equations with initial conditions involving ψ -Hilfer fractional derivative.