A New Result Concerning Nonlocal Controllability of Hilfer Fractional Stochastic Differential Equations via almost Sectorial Operators

Sivasankar, Sivajiganesan; Udhayakumar, R.; Kishor, Muchenedi Hari; Alhazmi, Sharifah E.; Al‐Omari, Shrideh

doi:10.3390/math11010159

Cited by 12 publications

(5 citation statements)

References 42 publications

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“…In this paper, we use Sadovskii fixed point theorem in [21] to prove the existence results for impulsive neutral integrodifferential systems. The fixed point technique, and measures of noncompactness have been disscussed in this research work as it is mentionned in [22]. Among the foremost fundamental qualitative properties of differential systems, my paper is especially concerned into existence of solutions for neutral impulsive stochastic differential systems where some researchers have been introduced this theory such as [23].…”

Section: Impulsive Differential Systemsmentioning

confidence: 99%

A Study on Stochastic Differential Equation Using Fractional Power of Operator in the Semigroup Theory

Hagenimana,

Uwiliniyimana,

Umuraza

2023

JAMP

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Stochastic differential equation (SDE) is an ordinary differential equation with a stochastic process that can model the unpredictable real-life behavior of any continuous systems. It is the combination of differential equations, probability theory, and stochastic processes. Stochastic differential equations arise in modeling a variety of random dynamic phenomena in physical, biological and social process. The SDE theory is traditionally used in physical science and financial mathematics. Recently, more researchers have been conducted in the application of SDE theory to various areas of engineering. This dissertation is mainly concerned with the existence of mild solutions for impulsive neutral stochastic differential equations with nonlocal conditions in Hilbert spaces. The results are obtained by using fractional powers of operator in the semigroup theory and Sadovskii fixed point theorem.

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Section: Impulsive Differential Systemsmentioning

confidence: 99%

A Study on Stochastic Differential Equation Using Fractional Power of Operator in the Semigroup Theory

Hagenimana,

Uwiliniyimana,

Umuraza

2023

JAMP

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“…Ravikumar et al [10] discussed the null controllability of nonlocal Sobolev-type Hilfer fractional stochastic differential system driven by fractional Brownian motion and Poisson jumps. Sivasankar et al [11] investigated the nonlocal controllability of Hilfer fractional stochastic differential equations via almost sectorial operators. For further information on this topic, we refer to [12][13][14][15] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Hilfer Fractional Neutral Stochastic Differential Inclusions with Clarke’s Subdifferential Type and fBm: Approximate Boundary Controllability

Nandhaprasadh,

Udhayakumar

2024

Contemp. Math.

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In this paper, the approximate boundary controllability of Hilfer fractional neutral stochastic differential inclusions with fractional Brownian motion (fBm) and Clarke’s subdifferential in Hilbert space is discussed. The existence of a mild solution of Hilfer fractional neutral stochastic differential inclusions with fractional Brownian motion and Clarke’s subdifferential is proved by using fractional calculus, compact semigroups, the fixed point theorem, stochastic analysis, and multivalued maps. The required conditions for the approximate boundary controllability of this system are defined according to a corresponding linear system that is approximately controllable. To demonstrate how our primary findings may be used, a final example is provided.

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“…Recently, in [21][22][23] discussed the approximate controllability of fractional stochastic differential systems of order 1 < r < 2. It is possible to support discussions of theory and applications related to controllability by citing the research papers [24][25][26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

A Study on Approximate Controllability of Ψ-Caputo Fractional Differential Equations with Impulsive Effects

Varun Bose,

Udhayakumar,

Muthukumaran

et al. 2024

Contemp. Math.

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In this article, we studied the approximate controllability of Ψ-Caputo fractional differential systems. We prove the sufficient conditions for an abstract Cauchy problem invloving infinite delay, impulsive and nonlocal conditions. The result is shown by means of the infinitesimal operator, semigroup theory, fractional calculus, and Schauder’s fixed point theorem. First, we prove the existence of the mild solution and demonstrate that the Ψ-Caputo fractional system is approximately controllable. Finally, an example is given to analyse the obtained results.

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A New Result Concerning Nonlocal Controllability of Hilfer Fractional Stochastic Differential Equations via almost Sectorial Operators

Cited by 12 publications

References 42 publications

A Study on Stochastic Differential Equation Using Fractional Power of Operator in the Semigroup Theory

A Study on Stochastic Differential Equation Using Fractional Power of Operator in the Semigroup Theory

Hilfer Fractional Neutral Stochastic Differential Inclusions with Clarke’s Subdifferential Type and fBm: Approximate Boundary Controllability

A Study on Approximate Controllability of Ψ-Caputo Fractional Differential Equations with Impulsive Effects

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