Non-Instantaneous Impulsive BVPs Involving Generalized Liouville–Caputo Derivative

Salem, Ahmed; Abdullah, Sanaa

doi:10.3390/math10030291

Cited by 11 publications

(2 citation statements)

References 30 publications

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“…Ordinary differentiation and integration of arbitrary order, which may be non-integer, are generalized in fractional calculus. Many studies have focused on differential equations of fractional order [1][2][3]. Many definitions of fractional integrals and derivatives may be found in the literature, ranging from the most well-known Riemann-Liouville (R-L) and Caputo-type fractional derivatives to others like the Hadamard fractional derivative, the Katugampola fractional derivative, the Hilfer fractional derivative, and so on.…”

Section: Introductionmentioning

confidence: 99%

Finite-Time Stability to Fractional Delay Cauchy Problem of Hilfer Type

Salem,

Babusail,

El-Shahed

et al. 2023

Contemp. Math.

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The purpose of this work is to look at the solution’s representation for the non-homogeneous fractional timedelay Cauchy problem of Hilfer type in terms of the cosine and sine fractional delayed matrices of two parameters. The solutions are determined using the constant variation approach. Following that, finite-time stability under moderate circumstances is examined. At last, an example is offered to show how the theoretical results may be used.

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Section: Introductionmentioning

confidence: 99%

Finite-Time Stability to Fractional Delay Cauchy Problem of Hilfer Type

Salem,

Babusail,

El-Shahed

et al. 2023

Contemp. Math.

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“…Instantaneous impulses are the first type; alterations of this kind last just briefly. The second kind is non-instantaneous impulses, in which the impulsive activity begins at an arbitrarily fixed moment and continues for a certain amount of time [19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Total Controllability for a Class of Fractional Hybrid Neutral Evolution Equations with Non-Instantaneous Impulses

Salem

Alharbi

2023

Fractal Fract

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This study demonstrates the total control of a class of hybrid neutral fractional evolution equations with non-instantaneous impulses and non-local conditions. The boundary value problem with non-local conditions is created using the Caputo fractional derivative of order 1<α≤2. In order to create novel, strongly continuous associated operators, the infinitesimal generator of the sine and cosine families is examined. Additionally, two approaches are used to discuss the solution’s total controllability. A compact strategy based on the non-linear Leray–Schauder alternative theorem is one of them. In contrast, a measure of a non-compactness technique is implemented using the Sadovskii fixed point theorem with the Kuratowski measure of non-compactness. These conclusions are applied using simulation findings for the non-homogeneous fractional wave equation.

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Controllability results to non-instantaneous impulsive with infinite delay for generalized fractional differential equations

Salem¹,

Abdullah²

2023

Alexandria Engineering Journal

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Non-Instantaneous Impulsive BVPs Involving Generalized Liouville–Caputo Derivative

Cited by 11 publications

References 30 publications

Finite-Time Stability to Fractional Delay Cauchy Problem of Hilfer Type

Finite-Time Stability to Fractional Delay Cauchy Problem of Hilfer Type

Total Controllability for a Class of Fractional Hybrid Neutral Evolution Equations with Non-Instantaneous Impulses

Controllability results to non-instantaneous impulsive with infinite delay for generalized fractional differential equations

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