Approximate controllability results for abstract neutral integro-differential inclusions with infinite delay in Hilbert spaces

Vijayakumar, V.

doi:10.1093/imamci/dnw049

Cited by 28 publications

(25 citation statements)

References 43 publications

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“…Physical problems energize the investigation about the system with nonlocal conditions. Byszewski [51, 52], introduced the concept of nonlocal conditions for studying the existence of mild solutions and several researchers done enormous works inspired by these articles, one can refer [15–17, 19, 25, 26, 29–31, 46]. Consider the Sobolev‐type nonlocal Hilfer fractional system of the following form

D_{0^{+}}^{ν, ϖ} false[Ju false(t false) - F_{1} false(t, u_{t} false) false] = Au false(t false) + F_{2} (t,,, u_{t},,, \int_{0}^{t} e false(t, τ, u_{τ} false) italicd τ), t \in I = false[0, c false],

I_{0^{+}}^{false(1 - ν false) false(1 - ϖ false)} u false(t false) = ϕ false(t false) + g false(u_{t_{1}}, u_{t_{2}}, u_{t_{3}}, \dots, u_{t_{n}} false) \in {scriptB}_{l},

where 0 < t 1 < t 2 < t 3 < ⋯ < t n ≤ c ,

g : {scriptB}_{l}^{n} \to {scriptB}_{l}

and satisfies the following:…”

Section: Nonlocal Conditionsmentioning

confidence: 99%

“…This system could apply to abundant models in wave propagation, signal processing, robotics, and so on. It defines more about the theory and details of applications also, and the readers can review the monographs [1][2][3][4][5][6][7][8][9] and the research articles related to the theory of fractional differential systems [10][11][12][13][14][15][16][17][18][19][20][21]. Hilfer [22] introduced another type of fractional derivative, which involving Riemann-Liouville and Caputo fractional derivative.…”

Section: Introductionmentioning

confidence: 99%

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A new exploration on existence of Sobolev‐type Hilfer fractional neutral integro‐differential equations with infinite delay

Vijayakumar

Udhayakumar

2020

Numerical Methods Partial

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This article is primarily focusing on the existence of Sobolev-type Hilfer fractional neutral integro-differential systems via measure of noncompactness. We study our primary outcomes by employing fractional calculus, measure of noncompactness and fixed point technique. First, we discuss the existence of mild solution for the fractional evolution system. Then, we extend our results to discuss the system with nonlocal conditions. Finally, we provide theoretical and practical applications to illustrate the obtained theory.

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D_{0^{+}}^{ν, ϖ} false[Ju false(t false) - F_{1} false(t, u_{t} false) false] = Au false(t false) + F_{2} (t,,, u_{t},,, \int_{0}^{t} e false(t, τ, u_{τ} false) italicd τ), t \in I = false[0, c false],

I_{0^{+}}^{false(1 - ν false) false(1 - ϖ false)} u false(t false) = ϕ false(t false) + g false(u_{t_{1}}, u_{t_{2}}, u_{t_{3}}, \dots, u_{t_{n}} false) \in {scriptB}_{l},

where 0 < t 1 < t 2 < t 3 < ⋯ < t n ≤ c ,

g : {scriptB}_{l}^{n} \to {scriptB}_{l}

and satisfies the following:…”

Section: Nonlocal Conditionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A new exploration on existence of Sobolev‐type Hilfer fractional neutral integro‐differential equations with infinite delay

Vijayakumar

Udhayakumar

2020

Numerical Methods Partial

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“…Kumar et al [17] investigated the approximate controllability of fractional order semilinear systems with bounded delay. Vijayakumar [30] explored the approximate controllability results for the inclusion differential systems with infinite delay in Hilbert spaces. However, to the best of our knowledge, there are no results on the approximate controllability of multi-term time-fractional differential stochastic differential inclusions as treated in the current paper.…”

Section: Introductionmentioning

confidence: 99%

Approximate controllability of multi-term time-fractional stochastic differential inclusions with nonlocal conditions

Kumar¹,

Pandey²

2019

Malaya J. Mat.

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“…Hence this is a stronger notion of controllability. For classical nonlinear control system the fixed point methods are widely used as a tool to study the controllability problem [6,12,15,19,23,26,28,34,40,41]. In the mathematical perspective, the issues of exact and approximate controllability are to be distinguished.…”

Section: Introductionmentioning

confidence: 99%

Approximate controllability of second-order nonlocal impulsive partial functional integro-differential evolution systems in Banach spaces

Nagaraj¹,

Kavitha

Băleanu

et al. 2019

Filomat

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This manuscript is involved with a class of second-order impulsive partial functional integrodifferential evolution equations with nonlocal conditions in Banach spaces. Sufficient conditions ensuring the existence and approximate controllability of mild solutions are established. Theory of cosine family, Banach contraction principle and Leray-Schauder nonlinear alternative fixed point theorem are employed for achieving the required results. An example is analyzed to illustrate the effectiveness of the outcome.

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Approximate controllability results for abstract neutral integro-differential inclusions with infinite delay in Hilbert spaces

Cited by 28 publications

References 43 publications

A new exploration on existence of Sobolev‐type Hilfer fractional neutral integro‐differential equations with infinite delay

A new exploration on existence of Sobolev‐type Hilfer fractional neutral integro‐differential equations with infinite delay

Approximate controllability of multi-term time-fractional stochastic differential inclusions with nonlocal conditions

Approximate controllability of second-order nonlocal impulsive partial functional integro-differential evolution systems in Banach spaces

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