Existence Results of Global Solutions for a Coupled Implicit Riemann-Liouville Fractional Integral Equation via the Vector Kuratowski Measure of Noncompactness

Laksaci, Noura; Boudaoui, Ahmed; Shatanawi, Wasfı; Shatnawi, Taqi A. M.

doi:10.3390/fractalfract6030130

Cited by 4 publications

(2 citation statements)

References 15 publications

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“…Recently, many authors combined the concept of a measure of noncompactness and matrices that converge to zero, R. Graef et al in [15] gave the vector versions of Sadovskii's fixed point theorem. In [23], N. Laksaci et al generalized Darbo's fixed point theorem for iterated Operators.…”

Section: Introduction Milman and Myshkismentioning

confidence: 99%

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Existence and Ulam-Hyers-Rassias stability of mild solutions for impulsive integro-differential systems via resolvent operators

Bensalem,

Salim,

Benchohra

et al. 2023

MFC

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The aim of this paper is to present existence, Ulam-Hyers-Rassias stability and continuous dependence on initial conditions for the mild solution of impulsive integro-differential systems via resolvent operators. Our analysis is based on fixed point theorem with generalized measures of noncompactness, this approach is combined with the technique that uses convergence to zero matrices in generalized Banach spaces. An example is presented to illustrate the efficiency of the result obtained.

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Section: Introduction Milman and Myshkismentioning

confidence: 99%

“…Motivated by works [9,15,23], we will investigate the existence and stability of mild solutions for impulsive integro-differential system via resolvent operators of the form:…”

Section: Introduction Milman and Myshkismentioning

confidence: 99%

Existence and Ulam-Hyers-Rassias stability of mild solutions for impulsive integro-differential systems via resolvent operators

Bensalem,

Salim,

Benchohra

et al. 2023

MFC

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On Using Piecewise Fractional Differential Operator to Study a Dynamical System

Khan

Alrabaiah

et al. 2023

Axioms

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This research work is devoted to undertaking a dynamical system representing SARS-CoV-19 disease under the concept of piecewise fractional-order derivative using the Caputo concept since long-memory and short-memory terms are not well explained by ordinary fractional differential equations. It has been found that for such disruption, piecewise operators of fractional derivatives have been found useful in many cases. Therefore, we study a compartmental model of susceptible and infected individuals under the concept of piecewise derivative. We establish the existence theory of the considered model by using some Banach and Schauder fixed-point theorems. Keeping the importance of stability, a pertinent result related to the said area is also developed. The said concept of stability is based on the concept given by Ulam and Hyers. Further, to derive the numerical results, we use the Euler method to develop a numerical scheme for the considered model. Using real available data, we have presented various graphical presentations of two compartments against different fractional orders and various values of isolation parameters. The crossover behaviors in the dynamics can be clearly observed, which is explained by the piecewise operators, not the usual fractional-order derivative.

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On the Controllability of Coupled Nonlocal Partial Integrodifferential Equations Using Fractional Power Operators

Litimein,

Huang,

Ouahab

et al. 2024

Fractal Fract

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In this research paper, we investigate the controllability in the α-norm of a coupled system of integrodifferential equations with state-dependent nonlocal conditions in generalized Banach spaces. We establish sufficient conditions for the system’s controllability using resolvent operator theory introduced by Grimmer, fractional power operators, and fixed-point theorems associated with generalized measures of noncompactness for condensing operators in vector Banach spaces. Finally, we present an application example to validate the proposed methodology in this research.

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Existence Results of Global Solutions for a Coupled Implicit Riemann-Liouville Fractional Integral Equation via the Vector Kuratowski Measure of Noncompactness

Cited by 4 publications

References 15 publications

Existence and Ulam-Hyers-Rassias stability of mild solutions for impulsive integro-differential systems via resolvent operators

Existence and Ulam-Hyers-Rassias stability of mild solutions for impulsive integro-differential systems via resolvent operators

On Using Piecewise Fractional Differential Operator to Study a Dynamical System

On the Controllability of Coupled Nonlocal Partial Integrodifferential Equations Using Fractional Power Operators

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