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چکیده
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The notion of $\mathcal{A}$-condensing operators via measure of noncompactness is proposed, which retains the existing classes of condensing operators. Results concerning the existence of best proximity point (pair) of cyclic (noncyclic) $\mathcal{A}$-condensing operators along with the coupled best proximity point theorem for cyclic $\mathcal{A}$-condensing operators have been formulated. An application to $(k, \gimel)$-Hilfer fractional differential equation of order $2< p<3$, type $q\in [0,1]$ satistfying some boundary conditions is presented. The concerned paper is first to investigate the optimum solution of such a generalized fractional differential equation. The hypothesis involved in the investigation is independent of the incorporated measure of noncompactness, thereby making our result better in application than that present in the literature. Moreover, added numerical examples validates the theoretical conclusions.
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