Some sufficient conditions of existence and trajectory controllability for impulsive and initial value fractional order functional differential equations

Gautam, Ganga Ram; Kumar, Manoj; Dwivedi, Arpit; Rani, Gunjan; Arya, Namrata; Jaimala,

doi:10.1016/j.rico.2023.100237

Results in Control and Optimization

2023

DOI: 10.1016/j.rico.2023.100237

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Some sufficient conditions of existence and trajectory controllability for impulsive and initial value fractional order functional differential equations

Ganga Ram Gautam

Manoj Kumar

Arpit Dwivedi

et al.

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2024

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Cited by 2 publications

(1 citation statement)

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“…The matter of control in nonlinear systems has garnered significant attention in recent times. Several control mechanisms, including adaptive PID control, were proposed for a range of different systems, 38 sliding mode control, intelligent control, backstepping control, hybrid control, active disturbance rejection control, impulsive control, 39 event-triggered control 40 and optimal control. 41 Several notable research has been conducted to address the challenges posed by the formation of unknown functions in real-world systems driven by practical demands and theoretical complexities.…”

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confidence: 99%

A novel adaptive control design for exponential stabilization of memristor‐based CVNNs with time‐varying delays using matrix measures

Jayanthi,

Santhakumari,

Grienggrai Rajchakit

et al. 2024

Int J Numerical Modelling

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The present study introduces a new adaptive control framework that aims to attain exponential stability in complex‐valued neural network systems utilizing memristors while accounting for time‐varying delays. The control issues in systems of this nature are mostly attributed to the presence of memristors and time‐varying latency. To overcome these challenges and achieve stabilization outcomes, a methodology is employed that integrates adaptive control approaches inside a matrix‐based framework. This study employs Lyapunov's stability theory to establish exponential stabilization conditions and conduct convergence analysis. The efficacy of the suggested control algorithm in achieving exponential stabilization and robustness under varied delays is demonstrated through numerical simulations.

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mentioning

confidence: 99%

A novel adaptive control design for exponential stabilization of memristor‐based CVNNs with time‐varying delays using matrix measures

Jayanthi,

Santhakumari,

Grienggrai Rajchakit

et al. 2024

Int J Numerical Modelling

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On a new structure of multi-term Hilfer fractional impulsive neutral Levin-Nohel integrodifferential system with variable time delay

Abdeljawad,

Thabet,

Kedim

et al. 2024

MATH

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<abstract><p>The Levin-Nohel equations play key roles in the interpretation of real phenomena and have interesting applications in engineering and science areas, such as mathematical physics, mathematical biology, image processing, and numerical analyses. This article investigates a new structure for the delay neutral Levin-Nohel integrodifferential (NLNID) system via a Hilfer fractional derivative and is supplemented by initial and instantaneous impulse conditions. A fractional integral equation corresponding to the proposed system is derived and used to prove the existence and uniqueness of the solution with the help of the Banach contraction principle. Additionally, the Ulam-Hyers-Mittag-Leffler (UHML) stability is studied by utilizing the generalized Gronwall's inequality and nonlinear analysis issues. As a consequence, the Ulam-Hyers (UH) stability and generalized UH are also deduced. Furthermore, the Riemann-Liouville ($ \mathcal{R.L.} $) and Caputo fractional versions of the proposed system are discussed. Finally, numerical applications supported with tables and graphics are provided to test the exactitude of the findings.</p></abstract>

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Some sufficient conditions of existence and trajectory controllability for impulsive and initial value fractional order functional differential equations

Cited by 2 publications

References 23 publications

A novel adaptive control design for exponential stabilization of memristor‐based CVNNs with time‐varying delays using matrix measures

A novel adaptive control design for exponential stabilization of memristor‐based CVNNs with time‐varying delays using matrix measures

On a new structure of multi-term Hilfer fractional impulsive neutral Levin-Nohel integrodifferential system with variable time delay

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