Existence Theorems for Fractional Semilinear Integrodifferential Equations with Noninstantaneous Impulses and Delay

Zhu, Bo; Zhu, Minhui

doi:10.1155/2020/2914269

Cited by 3 publications

(3 citation statements)

References 35 publications

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“…Currently, the theory of fractional calculus has been extensively employed in disciplines such as viscoelasticity and rheology, physics, signal processing, control engineering, etc. For further information regarding these studies, please go through [1][2][3][4][5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Approximate Controllability for a Class of Semi-Linear Fractional Integro-Differential Impulsive Evolution Equations of Order 1 < α < 2 with Delay

Zhao

2023

Mathematics

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This article is mainly concerned with the approximate controllability for some semi-linear fractional integro-differential impulsive evolution equations of order 1<α<2 with delay in Banach spaces. Firstly, we study the existence of the PC-mild solution for our objective system via some characteristic solution operators related to the Mainardi’s Wright function. Secondly, by using the spatial decomposition techniques and the range condition of control operator B, some new results of approximate controllability for the fractional delay system with impulsive effects are obtained. The results cover and extend some relevant outcomes in many related papers. The main tools utilized in this paper are the theory of cosine families, fixed-point strategy, and the Grönwall-Bellman inequality. At last, an example is given to demonstrate the effectiveness of our research results.

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Section: Introductionmentioning

confidence: 99%

Approximate Controllability for a Class of Semi-Linear Fractional Integro-Differential Impulsive Evolution Equations of Order 1 < α < 2 with Delay

Zhao

2023

Mathematics

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“…Norouzi et al [17] proved the existence and uniqueness solution for a ψ-Hilfer neutral fractional semilinear equation with infinite delay, and the outcomes were obtained by the semigroup operator, Banach fixed-point theorem, and nonlinear alternative of the Leray-Schauder type. For more contributions to the literature, see [18][19][20][21][22] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Fractional Evolution Equations with Infinite Time Delay in Abstract Phase Space

2022

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In the presented research, the uniqueness and existence of a mild solution for a fractional system of semilinear evolution equations with infinite delay and an infinitesimal generator operator are demonstrated. The generalized Liouville–Caputo derivative of non-integer-order 1<α≤2 and the parameter 0<ρ<1 are used to establish our model. The ρ-Laplace transform and strongly continuous cosine and sine families of uniformly bounded linear operators are adapted to obtain the mild solution. The Leray–Schauder alternative theorem and Banach contraction principle are used to demonstrate the mild solution’s existence and uniqueness in abstract phase space. The results are applied to the fractional wave equation.

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“…Delay PDEs with fractional derivatives have recently been studied using various numerical and analytical techniques such as [4][5][6][7][8]. It was pointed out in [9] that the derivatives of the dependent variable in the neutral type delay differential equations are both with and without time delays.…”

Section: Introductionmentioning

confidence: 99%

Interpolating Stabilized Element Free Galerkin Method for Neutral Delay Fractional Damped Diffusion-Wave Equation

Abbaszadeh

Dehghan

Zaky

et al. 2021

Journal of Function Spaces

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A numerical solution for neutral delay fractional order partial differential equations involving the Caputo fractional derivative is constructed. In line with this goal, the drift term and the time Caputo fractional derivative are discretized by a finite difference approximation. The energy method is used to investigate the rate of convergence and unconditional stability of the temporal discretization. The interpolation of moving Kriging technique is then used to approximate the space derivative, yielding a meshless numerical formulation. We conclude with some numerical experiments that validate the theoretical findings.

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Existence Theorems for Fractional Semilinear Integrodifferential Equations with Noninstantaneous Impulses and Delay

Cited by 3 publications

References 35 publications

Approximate Controllability for a Class of Semi-Linear Fractional Integro-Differential Impulsive Evolution Equations of Order 1 < α < 2 with Delay

Approximate Controllability for a Class of Semi-Linear Fractional Integro-Differential Impulsive Evolution Equations of Order 1 < α < 2 with Delay

Fractional Evolution Equations with Infinite Time Delay in Abstract Phase Space

Interpolating Stabilized Element Free Galerkin Method for Neutral Delay Fractional Damped Diffusion-Wave Equation

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