Asymptotic stability of fractional order (1, 2] stochastic delay differential equations in Banach spaces

A Singh, A Shukla, V Vijayakumar… - Chaos, Solitons & …, 2021 - Elsevier
In this article, we discuss the asymptotic stability and mean square stability of stochastic
differential equations of fractional-order 1< α≤ 2. We have considered the family of …

A new exploration on the existence and approximate controllability for fractional semilinear impulsive control systems of order r∈(1, 2)

A Shukla, V Vijayakumar, KS Nisar - Chaos, Solitons & Fractals, 2022 - Elsevier
In this article, we mainly focus on the existence and approximate controllability results for the
fractional semilinear impulsive control system of order r∈(1, 2). We consider two different …

[PDF][PDF] New results on controllability of fractional evolution systems with order α∈(1, 2)

Y Zhou, JW He - Evol. Equ. Control Theory, 2021 - researchgate.net
This paper addresses some interesting results of mild solutions to fractional evolution
systems with order α∈(1, 2) in Banach spaces as well as the controllability problem. Firstly …

New results on exact controllability of a class of fractional neutral integro-differential systems with state-dependent delay in Banach spaces

C Ravichandran, N Valliammal, JJ Nieto - Journal of the Franklin Institute, 2019 - Elsevier
This article deals with the use of Krasnoselskii's fixed point theorem and Leray–Schauder
alternative theorem combined with resolvent operator and some analytical methods to …

New discussion on approximate controllability results for fractional Sobolev type Volterra‐Fredholm integro‐differential systems of order 1 < r < 2

V Vijayakumar, C Ravichandran… - … Methods for Partial …, 2024 - Wiley Online Library
In our article, we are primarily concentrating on approximate controllability results for
fractional Sobolev type Volterra‐Fredholm integro‐differential inclusions of order 1< r< 2. By …

Existence and optimal control problem for semilinear fractional order (1, 2] control system

R Patel, A Shukla, SS Jadon - Mathematical Methods in the …, 2024 - Wiley Online Library
In this article, we have derived some sufficient conditions for existence of optimal control for
semilinear control system of fractional order (1, 2] in Hilbert space. We have discussed …

Controllability results for fractional semilinear delay control systems

A Shukla, R Patel - Journal of Applied Mathematics and Computing, 2021 - Springer
In this article, we have presented the controllability relationship between the semilinear
control system of fractional order (1, 2 with delay and that of the semilinear control system …

Results on existence and controllability results for fractional evolution inclusions of order 1 < r < 2 with Clarke's subdifferential type

M Mohan Raja, V Vijayakumar… - … Methods for Partial …, 2024 - Wiley Online Library
In our paper, we primarily concentrate on the existence and controllability results for
fractional evolution inclusions of order 1< r< 2 with Clarke's subdifferential type. By applying …

Results on approximate controllability of fractional stochastic Sobolev‐type Volterra–Fredholm integro‐differential equation of order 1 < r < 2

C Dineshkumar, R Udhayakumar - Mathematical Methods in …, 2022 - Wiley Online Library
The main motivation of our conversation is the approximate controllability of fractional
stochastic Sobolev‐type Volterra–Fredholm integro‐differential equation of order 1< r< 2 …

Existence of mild solutions to Hilfer fractional evolution equations in Banach space

JVC Sousa, F Jarad, T Abdeljawad - Annals of Functional Analysis, 2021 - Springer
In this paper, we investigate the existence of mild solutions to semilinear evolution fractional
differential equations with non-instantaneous impulses, using the concepts of …