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 …

Controllability of discrete-time semilinear Riemann–Liouville-like fractional equations

M Malik, V Vijayakumar, A Shukla - Chaos, Solitons & Fractals, 2023 - Elsevier
This article utilizes the Riemann–Liouville-like fractional operator to investigate certain
sufficient conditions for the approximate controllability of discrete-time fractional evolution …

An investigation on the optimal control for Hilfer fractional neutral stochastic integrodifferential systems with infinite delay

M Johnson, V Vijayakumar - Fractal and Fractional, 2022 - mdpi.com
The main concern of this manuscript is to study the optimal control problem for Hilfer
fractional neutral stochastic integrodifferential systems with infinite delay. Initially, we …

A Note on the Existence and Controllability Results for Fractional Integrodifferential Inclusions of Order with Impulses

M Mohan Raja, A Shukla, JJ Nieto… - Qualitative Theory of …, 2022 - Springer
This paper investigates the issue of existence and approximate controllability results for
impulsive fractional differential inclusions with delay of order r∈(1, 2] in Banach space. To …

An operational matrix based scheme for numerical solutions of nonlinear weakly singular partial integro-differential equations

S Behera, SS Ray - Applied Mathematics and Computation, 2020 - Elsevier
In this article, we introduce an operational matrix scheme based on two-dimensional
wavelets for the Volterra weakly singular nonlinear partial integro-differential equations. By …

Controllability of a second-order non-autonomous stochastic semilinear system with several delays in control

A Afreen, A Raheem, A Khatoon - Chaos, Solitons & Fractals, 2022 - Elsevier
This paper studies a second-order non-autonomous semilinear stochastic differential
equation with several constant point delays in control. We prove the mild solution's existence …

Approximate controllability of semilinear fractional stochastic control system

A Shukla, N Sukavanam, DN Pandey - Asian-European Journal of …, 2018 - World Scientific
The objective of this paper is to present some sufficient conditions for approximate
controllability of semilinear fractional stochastic control system with delay. The results hold …

Approximate Controllability of Fractional Semilinear Stochastic System of Order α∈ (1,2

A Shukla, N Sukavanam, DN Pandey - Journal of Dynamical and Control …, 2017 - Springer
A family of dynamical control systems described by nonlinear fractional of order (1, 2]
stochastic differential equations in L p spaces is considered. We discussed the approximate …

A discussion on boundary controllability of nonlocal impulsive neutral integrodifferential evolution equations

K Kumar, R Patel, V Vijayakumar… - … Methods in the …, 2022 - Wiley Online Library
Sufficient conditions for boundary controllability of nonlocal impulsive neutral
integrodifferential evolution equations are explored. In the first problem, the outcomes are …

The controllability of damped fractional differential system with impulses and state delay

M Nawaz, J Wei, J Sheng, AU Khan - Advances in Difference Equations, 2020 - Springer
We discuss the controllability for a damped fractional differential system with impulses and
state delay, which involves Caputo fractional derivatives. Deriving the condition based on …