Solvability of an infinite system of fractional differential equations with p-Laplacian operator in a new tempered sequence space

Mursaleen, Mohammad; Savaş, Ekrem

doi:10.1007/s11868-023-00552-4

Cited by 2 publications

(1 citation statement)

References 33 publications

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“…The DEs of the HFDE, ψ-HFDE, and (k, ‫-)ג‬HFDE types, because they provide significant generalizations, are very useful in solving different types of differential equations. For more details of these types of generalizations and results of controllability involving ψ-HFDEs refer to [15][16][17][18][19][20][21][22] and references therein. The work referenced above inspired us to propose a most generalized version of the Hilfer derivative, the so-called (k, ‫-)ג‬Hilfer fractional derivative.…”

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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