Existence and Controllability of Fractional Neutral Integro-Differential Systems With State-Dependent Delay in Banach Spaces

Kailasavalli, S.; Suganya, S.; Arjunan, M. Mallika

doi:10.12941/jksiam.2016.20.051

Cited by 3 publications

(1 citation statement)

References 28 publications

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“…In recent years, the controllability problems for various linear and nonlinear deterministic and stochastic dynamic systems have been studied in many publications using different method, we refer the reader to [2,6,24]. In addition, Kailasavalli et al [14] acknowledged the existence and controllability of fractional neutral integro-differential systems with SDD with Banach contraction and resolvent operator technique as the main reference. Dabas et al [10] studied the existence, uniqueness and continuous dependence of a mild solution for an impulsive neutral fractional order differential equation with infinite delay.…”

Section: Introductionmentioning

confidence: 99%

A study on controllability of impulsive fractional evolution equations via resolvent operators

Gou

2021

Bound Value Probl

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In this article, we study the controllability for impulsive fractional integro-differential evolution equation in a Banach space. The discussions are based on the Mönch fixed point theorem as well as the theory of fractional calculus and the $(\alpha ,\beta )$ ( α , β ) -resolvent operator, we concern with the term $u'(\cdot )$ u ′ ( ⋅ ) and finding a control v such that the mild solution satisfies $u(b)=u_{b}$ u ( b ) = u b and $u'(b)=u'_{b}$ u ′ ( b ) = u b ′ . Finally, we present an application to support the validity study.

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Section: Introductionmentioning

confidence: 99%

A study on controllability of impulsive fractional evolution equations via resolvent operators

Gou

2021

Bound Value Probl

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

Vijayakumar¹

2016

IMA J Math Control Info

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A New Investigation on Fractional-Ordered Neutral Differential Systems with State-Dependent Delay

Valliammal¹,

Ravichandran²,

Hammouch

et al. 2019

International Journal of Nonlinear Sciences and Numerical Simulation

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Fractional differential equations with delay behaviors occur in fields like physical and biological ones with state-dependent delay or nonconstant delay and has drawn the attention of researchers. The main goal of the present work is to study the existence of mild solutions of neutral differential system along state-dependent delay in Banach space. By employing the fractional theory, noncompact measure and Mönch’s theorem, we investigate the existence results for neutral differential equations of fractional order with state-dependent delay. An illustration of derived results is offered.

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Existence and Controllability of Fractional Neutral Integro-Differential Systems With State-Dependent Delay in Banach Spaces

Cited by 3 publications

References 28 publications

A study on controllability of impulsive fractional evolution equations via resolvent operators

A study on controllability of impulsive fractional evolution equations via resolvent operators

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

A New Investigation on Fractional-Ordered Neutral Differential Systems with State-Dependent Delay

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