Muthuvel K

EDUCATION

M.Sc., M.Phil.., Ph.D.

RESEARCH, TEACHING, or OTHER INTERESTS

Control and Optimization, Applied Mathematics, Computational Mathematics, Numerical Analysis

Scopus Publications

Relative controllability for ψ−Caputo fractional delay control system
K. Muthuvel, K. Kaliraj, Kottakkaran Sooppy Nisar, V. Vijayakumar
Results in Control and Optimization, 2024
This paper resolves around relative controllability of ψ−fractional delayed differential equations in finite dimensional space. The Mittag Leffler type of ψ−delayed perturbation matrix function with two parameters exhibits the Grammian matrix of fractional delay system. Based on this Grammian matrix we derived the necessary and sufficient conditions for the linear system which is relatively controllable. The fixed point approach is applied for obtaining a controllability result for semilinear system. This concept can be applied to some examples in order to illustrate the efficacy of our results.
Existence of solution for Volterra–Fredholm type stochastic fractional integro-differential system of order μ∈(1,2) with sectorial operators
K. Kaliraj, K. Muthuvel
Mathematical Methods in the Applied Sciences, 2023
The mainspring of the study is to investigate the out‐turn of stochastic Volterra–Fredholm integro‐differential inclusion of order with sectorial operator of the type . The existence results of our proposed problem is derived by employing Martelli's fixed point approach. We do not limit the theoretical results of fractional stochastic equation to local condition but extend to nonlocal condition, and physical interpretation of our obtained results is proved with an appropriate illustration.
Relative Controllability of ψ-Caputo Fractional Neutral Delay Differential System
Kothandapani Muthuvel, Panumart Sawangtong, Kalimuthu Kaliraj
Fractal and Fractional, 2023
The aim of this work is to analyze the relative controllability and Ulamn–Hyers stability of the ψ-Caputo fractional neutral delay differential system. We use neutral ψ-delayed perturbation of the Mitttag–Leffler matrix function and Banach contraction principle to examine the Ulam–Hyers stability of our considered system. We formulate the Grammian matrix to establish the controllability results of the linear fractonal differential system. Further, we employ the fixed-point technique of Krasnoselskii’s type to establish the sufficient conditions for the relative controllability of a semilinear ψ-Caputo neutral fractional system. Finally, the theoretical study is validated by providing an application.
A study on the approximate controllability results of fractional stochastic integro-differential inclusion systems via sectorial operators
Kaliraj Kalimuthu, Kothandapani Muthuvel
International Journal of Optimization and Control Theories and Applications, 2023
The study deals with the findings of the outcome of the approximate controllability results of inclusion type fractional stochastic system in Banach space with the order of the fractional system varrho in (1,2). At first, we implement Bohnenblust-Karlin's fixed point technique to deduce the required conditions on which the fractional system with inital conditions is approximately controllable, and there by, we postulate the sufficient conditions for extending the obtained results to the system with nonlocal conditions.

RECENT SCHOLAR PUBLICATIONS

Relative controllability for ψ− Caputo fractional delay control system
K Muthuvel, K Kaliraj, KS Nisar, V Vijayakumar
Results in Control and Optimization 16, 100475 , 2024
2024
Citations: 22
Existence of solution for Volterra–Fredholm type stochastic fractional integro‐differential system of order μ ∈ (1, 2) with sectorial operators
K Kaliraj, K Muthuvel
Mathematical Methods in the Applied Sciences 46 (12), 13142-13154 , 2023
2023
Citations: 8
Relative controllability of ψ-Caputo fractional neutral delay differential system
K Muthuvel, P Sawangtong, K Kaliraj
Fractal and Fractional 7 (6), 437 , 2023
2023
Citations: 3
A study on the approximate controllability results of fractional stochastic integro-differential inclusion systems via sectorial operators.
K Kaliraj, K Muthuvel
International Journal of Optimization & Control: Theories & Applications 13 (2) , 2023
2023
Citations: 4

MOST CITED SCHOLAR PUBLICATIONS

Relative controllability for ψ− Caputo fractional delay control system
K Muthuvel, K Kaliraj, KS Nisar, V Vijayakumar
Results in Control and Optimization 16, 100475 , 2024
2024
Citations: 22
Existence of solution for Volterra–Fredholm type stochastic fractional integro‐differential system of order μ ∈ (1, 2) with sectorial operators
K Kaliraj, K Muthuvel
Mathematical Methods in the Applied Sciences 46 (12), 13142-13154 , 2023
2023
Citations: 8
A study on the approximate controllability results of fractional stochastic integro-differential inclusion systems via sectorial operators.
K Kaliraj, K Muthuvel
International Journal of Optimization & Control: Theories & Applications 13 (2) , 2023
2023
Citations: 4
Relative controllability of ψ-Caputo fractional neutral delay differential system
K Muthuvel, P Sawangtong, K Kaliraj
Fractal and Fractional 7 (6), 437 , 2023
2023
Citations: 3