Existence of solutions to Sobolev‐type partial neutraldifferential equations

Agarwal, Shruti; Bahuguna, D.

doi:10.1155/jamsa/2006/16308

Cited by 30 publications

(27 citation statements)

References 14 publications

(12 reference statements)

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“…As pointed out in [30], [36, p. 434], the study of the equations involving such effect is required as they display better consistency with the nature of the underlying process and predictive results. We mention in particular that, in [37] Agarwal and Bahuguna considered a neutral differential equation of Sobolev type involving a nonlocal initial condition and a time delay of type κ(t) = t − τ .…”

Section: Proposition 21 Assume That Q µ (T) Is a Solution Operator mentioning

confidence: 99%

On a class of retarded integro-differential equations with nonlocal initial conditions

Wang¹,

Chen²

2010

Computers & Mathematics with Applications

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a b s t r a c tOf concern is the following Cauchy problem for fractional integro-differential equations with time delay and nonlocal initial conditiongenerator of a solution operator on a complex Banach space X , the convolution integral in the equation is known as the Riemann-Liouville fractional integral, κ(t) : [0, +∞) → [−τ , +∞) representing the delay property, is a function, and H t is an operator defined from [−τ , 0] × C([−τ , 0], X ) into X for some T > 0 which constitutes a nonlocal condition. The local existence and uniqueness of mild solutions for the Cauchy problem, under various criteria, are proved. Moreover, we present an existence result of the global solution. Also an example is given to illustrate the applications of the abstract results.

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Section: Proposition 21 Assume That Q µ (T) Is a Solution Operator mentioning

confidence: 99%

On a class of retarded integro-differential equations with nonlocal initial conditions

Wang¹,

Chen²

2010

Computers & Mathematics with Applications

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“…Sobolev-type differential systems commonly manifest in the mathematical form of numerous physical phenomena similar to fluid flow over fissured rocks, thermodynamics. So on, we can refer to [19,[32][33][34][35][36][37][38][39][40]. To the best of our knowledge, the existence of mild solutions for Sobolev-type Hilfer fractional neutral integro-differential equations with infinite delay has not been studied in this connection.…”

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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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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“…Recently, fractional differential equations have been considered greatly by research community in various aspects due to its salient features for real world problems (see [1][2][3][4][5][6][7]). Controllability problems for different kinds of dynamical systems have been studied by several authors (see [8][9][10][11][12][13][14][15]) and references therein. Thus, the dynamical systems must be treated by the weaker concept of controllability, namely approximate controllability (see [16][17][18][19][20][21]).…”

Section: Introductionmentioning

confidence: 99%

Existence Solution and Controllability of Sobolev Type Delay Nonlinear Fractional Integro-Differential System

et al. 2019

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Fractional integro-differential equations arise in the mathematical modeling of various physical phenomena like heat conduction in materials with memory, diffusion processes, etc. In this manuscript, we prove the existence of mild solution for Sobolev type nonlinear impulsive delay integro-differential system with fractional order 1 < q < 2. We establish the sufficient conditions for the approximate controllability of Sobolev type nonlinear impulsive delay integro-differential system with fractional order 1 < q < 2. In addition, we prove the exact null controllability of Sobolev type nonlinear impulsive delay integro-differential system with fractional order 1 < q < 2. Finally, an example is given to illustrate the obtained results.

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Existence of solutions to Sobolev‐type partial neutraldifferential equations

Cited by 30 publications

References 14 publications

On a class of retarded integro-differential equations with nonlocal initial conditions

On a class of retarded integro-differential equations with nonlocal initial conditions

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

Existence Solution and Controllability of Sobolev Type Delay Nonlinear Fractional Integro-Differential System

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