A study on impulsive fractional hybrid evolution equations using sequence method

Gou, Haide; Li, Yongxiang

doi:10.1007/s40314-020-01239-y

Cited by 4 publications

(3 citation statements)

References 35 publications

(47 reference statements)

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“…By using a similar derivation to the mild solution of fractional impulsive systems in [9,38], we can transform system (3) into an equivalent integral expression…”

Section: Definition 1 ([35]mentioning

confidence: 99%

“…Controllability of control systems is an important component and research direction of control theory, as well as the foundation of optimal control and optimal estimation. In recent years, the controllability of various types of fractional dynamic systems, including fractional impulsive systems [9,10], delay syetems [11], stochastic systems [12,13], neutral systems [14], nonlocal systems [15], damped systems [16], integro-differential systems [17], measure evolution systems [18], etc., has been studied extensively and deeply. For example, in [10], the authors derived some new results of the total controllability (a type of exact controllability) for a fractional control system with non-instantaneous impulse by means of Krasnoselskii's fixed-point theorem.…”

Section: Introductionmentioning

confidence: 99%

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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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“…By using a similar derivation to the mild solution of fractional impulsive systems in [9,38], we can transform system (3) into an equivalent integral expression…”

Section: Definition 1 ([35]mentioning

confidence: 99%

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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“…Impulsive fractional order system (IFrOS) has become a focus of research and several hundreds of articles are found by searching the topic of IFrOS from Web of Science. For the IFrOS, its equivalent integral equation is key in studying numerical solution [18, 19], existence of solution [20–28], oscillation behavior [29, 30], periodic motion [31], solvability [32], asymptotic behavior of solution [33], stability [34–36], integral solution [37–45], and so on. Furthermore, the impulsive fractional partial differential order system (IFrPDOS) was firstly introduced in [46] by

({, \begin{matrix} left left \\ array_{(0 +, 0 +)}^{C} D_{(s, t)}^{e} Υ (s, t) = F (s, t, Υ (s, t)), & array (s, t) \in Θ, s \neq s_{j} (j = 1,2, \dots, J), \\ array Υ (s_{j}^{+}, t) - Υ (s_{j}^{-}, t) = U_{j} (Υ (s_{j}^{-}, t)), & array t \in [0, c], j = 1,2, \dots, J, \\ array Υ (s, 0) = η (s), Υ (0, t) = ξ \end{matrix})

…”

Section: Introductionmentioning

confidence: 99%

Impulsive fractional partial differential system and its correct equivalent integral equation

Zhang,

Liu,

Peng

et al. 2024

Math Methods in App Sciences

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It is found that there are two piecewise functions to satisfy the conditions in the impulsive fractional partial differential system (IFrPDS), which deduce that the three different equivalent integral equations of the IFrPDS given in the cited papers are inappropriate. Next, by applying two limit properties of the IFrPDS and the properties of piecewise function, the new formula of equivalent integral equation of the IFrPDS is discovered that is the integral equation with an arbitrary continuously differentiable function of on to reveal the non‐uniqueness of the IFrPDE's solution. Finally, an example is provided to expound the computation of the equivalent integral equation of the IFrPDS.

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Approximate controllability of third order dispersion systems

Gautam,

Shukla,

Johnson

et al. 2024

Bulletin des Sciences Mathématiques

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A study on impulsive fractional hybrid evolution equations using sequence method

Cited by 4 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

Impulsive fractional partial differential system and its correct equivalent integral equation

Approximate controllability of third order dispersion systems

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