Some inequalities on multi-functions for applying in the fractional Caputo–Hadamard jerk inclusion system

Etemad, Sina; Iqbal, Iram; Samei, Mohammad Esmael; Rezapour, Shahram; Alzabut, Jehad; Sudsutad, Weerawat; Göksel, İzzet

doi:10.1186/s13660-022-02819-8

Cited by 11 publications

(4 citation statements)

References 43 publications

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“…The technique used in this article can be used as a generalization in the area of solutions of nonlinear fractional and q-fractional differential equations via the bpp theory. The results of this research can establish more capabilities in the articles, such as [18,[38][39][40][41][42][43],…”

Section: Discussionmentioning

confidence: 69%

“…Proof If H ι stands for the natural projection of H into Y ι for ι = 1, 2, we set η(H) := max{η(H 1 ), η(H 2 )} then η becomes an MNC for Y 2 . Let us define by (40) then is cyclic on (C × C) ∪ (D × D). This is because, for any (v, w) in C × C and together with the cyclic nature of we have ( (v, w), (w, v))…”

Section: Then Affirms To Have a Coupled Bppmentioning

confidence: 99%

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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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Section: Discussionmentioning

confidence: 69%

Section: Then Affirms To Have a Coupled Bppmentioning

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

Self Cite

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show abstract

“…Fractional calculus indeed has wide range of applications including in mathematicsias well asiin various fieldsiof the modernisciences, such as bio-engineering [1,2], biological membranes [3,4], medicine [5], geophysics [6], demography [7], economy [8], and physics [9]. The field of fractional calculus was established in order to solveidifferentiali equations withifractional orderiderivatives.…”

Section: Introductionmentioning

confidence: 99%

Error Bounds for Fractional Integral Inequalities with Applications

Alqahtani,

Qaisar,

Munir

et al. 2024

Fractal Fract

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Fractional calculus has been a concept used to obtain new variants of some well-known integral inequalities. In this study, our main goal is to establish the new fractional Hermite–Hadamard, and Simpson’s type estimates by employing a differentiable function. Furthermore, a novel class of fractional integral related to prominent fractional operator (Caputo–Fabrizio) for differentiable convex functions of first order is proven. Then, taking this equality into account as an auxiliary result, some new estimation of the Hermite–Hadamard and Simpson’s type inequalities as generalization is presented. Moreover, few inequalities for concave function are obtained as well. It is observed that newly established outcomes are the extension of comparable inequalities existing in the literature. Additionally, we discuss the applications to special means, matrix inequalities, and the q-digamma function.

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“…Jerk systems have several applications in science [15][16][17][18][19]. Li and Zheng [15] proposed a 3-D jerk system with a sinusoidal term and noted that the system has an infinite number of equilibrium points.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation Analysis, Synchronization and FPGA Implementation of a New 3-D Jerk System with a Stable Equilibrium

et al. 2023

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This research paper addresses the modelling of a new 3-D chaotic jerk system with a stable equilibrium. Such chaotic systems are known to exhibit hidden attractors. After the modelling of the new jerk system, a detailed bifurcation analysis has been performed for the new chaotic jerk system with a stable equilibrium. It is shown that the new jerk system has multistability with coexisting attractors. Next, we apply backstepping control for the synchronization design of a pair of new jerk systems with a stable equilibrium taken as the master-slave chaotic systems. Lyapunov stability theory is used to establish the synchronization results for the new jerk system with a stable equilibrium. Finally, we show that the FPGA design of the new jerk system with a stable equilibrium can be implemented using the FPGA Zybo Z7-20 development board. The design of the new jerk system consists of multipliers, adders and subtractors. It is observed that the experimental attractors are in good agreement with simulation results.

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Some inequalities on multi-functions for applying in the fractional Caputo–Hadamard jerk inclusion system

Cited by 11 publications

References 43 publications

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

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

Error Bounds for Fractional Integral Inequalities with Applications

Bifurcation Analysis, Synchronization and FPGA Implementation of a New 3-D Jerk System with a Stable Equilibrium

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