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

Patle, Pradip Ramesh; Gabeleh, Moosa; Rakočević, Vladimir; Samei, Mohammad Esmael

doi:10.1007/s13398-023-01451-5

Cited by 3 publications

(1 citation statement)

References 27 publications

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“…Recently, valuable applications of MNC emphasizing the existence of solutions for a system of fractional differential and integral equations have been presented [23][24][25][26][27][28][29]. For example, Patle et al in [25], discussed the existence of optimal solutions of the following system of right-sided ψ-Hilfer fractional differential equations (ψ-HFDE) of arbitrary order with initial conditions…”

Section: Introductionmentioning

confidence: 99%

Optimum solution of $(k,\gimel )$-Hilfer FDEs by $\mathcal{A}$-condensing operators and the incorporated measure of noncompactness

Khokhar,

Patel,

Patle

et al. 2024

J Inequal Appl

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The notion of $\mathcal{A}$ A -condensing operators via the measure of noncompactness is proposed, which retains the existing classes of condensing operators. Results concerning the existence of the best proximity point (pair) of cyclic (noncyclic) $\mathcal{A}$ A -condensing operators along with the coupled best proximity-point theorem for cyclic $\mathcal{A}$ A -condensing operators have been formulated. An application to a $(k, \gimel )$ ( k , ℷ ) -Hilfer fractional differential equation of order $2< p<3$ 2 < p < 3 , type $q\in [0,1]$ q ∈ [ 0 , 1 ] satistfying some boundary conditions is presented. The paper is the 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 validate the theoretical conclusions.

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