An analysis of controllability results for nonlinear Hilfer neutral fractional derivatives with non-dense domain

Nisar, Kottakkaran Sooppy; Jothimani, K.; Kaliraj, K.; Ravichandran, C.

doi:10.1016/j.chaos.2021.110915

Cited by 78 publications

(17 citation statements)

References 27 publications

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“…Roughly speaking, controllability generally means that it is possible to steer a dynamical control system from an arbitrary initial state to an arbitrary final state using the set of admissible controls. In recent years, many authors have made fruitful achievements on exact controllability and approximate controllability of the different nonlinear dynamical problems with or without delay; one can refer to the researcher's articles 11,16–38 and references therein. In many cases, deterministic models often fluctuate due to environmental noise, which is random or at least appears to be so.…”

Section: Introductionmentioning

confidence: 99%

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

Dineshkumar

Udhayakumar

2022

Math Methods in App Sciences

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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. Using principles and ideas from stochastic analysis, the theory of cosine family, fractional calculus, and Banach fixed point techniques, the key findings are established. We begin by emphasizing the existence of mild solutions and then demonstrate the approximate controllability of the fractional stochastic control equation. We then apply our findings to the theory of nonlocal conditions. At last, an application is established for drawing the theory of the main results.

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Section: Introductionmentioning

confidence: 99%

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

Dineshkumar

Udhayakumar

2022

Math Methods in App Sciences

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“…We have also the so-called Atangana-Baleanu fractional operator and the Caputo-Fabrizio derivative which are known as the fractional operators with non-singular kernels [4,5]. These singular and non-singular derivatives appear in many papers with applications to physical modeling [2,6,7], biological modeling [8,9,10,11,12,13,14], sciences and engineering modeling [15,16,17,18,19], mathematical physics modeling [20,21,22,23,24,25,26], physics modeling [24,27] and others domains [28,29,30,31,32]. The field of fractional calculus is interesting but there also exist many questions without responses.…”

Section: Introductionmentioning

confidence: 99%

Second-grade fluid with Newtonian heating under Caputo fractional derivative: analytical investigations via Laplace transforms

Sene

2022

mmnsa

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In this paper, we consider the constructive equations of the fractional second-grade fluid. The considered fluid model is described by the Caputo derivative. The problem consists to determine the exact analytical solution using the Laplace transform method. The influence of the order of the used fractional operator has been presented in this paper. We also analyze the influence of the Prandtl number in the dynamics of the temperature distribution according to the variation of the order of the Caputo derivative. The impact of the second-grade parameter and the Grashof number in the dynamics of the velocity has been presented and discussed. The influences of the parameters used in the modeling have been interpreted in terms of a fractional context. In general, it is shown that the order of the fractional operator influences the diffusivity of the considered fluid. This influence can cause an increase or decrease in the temperature and velocity distributions. The main findings of the paper have been illustrated using the graphical representations of the considered distributions according to the order of the fractional operator.

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“…e epidemic models and their time-discrete variations have been studied by Allen [17] and Ghosh et al [18]. Several approaches towards fractional-order mathematical models of COVID-19 were studied by the authors Alqhtani et al [19], Valliammal and Ravichandran [20], Nisar et al [21], Vijayakumar et al [22], and Alderremy et al [23]. However, the aforementioned studies and references mostly contain explicit approaches with respect to time-discrete epidemic models.…”

Section: Introductionmentioning

confidence: 99%

“…e authors Hussain et al [13] discussed about the complex systems and network science approaches, along with technological advances and data availability, are becoming instrumental for the design of effective containment strategies. In a nonsense region, Hilfer's neutral fractional derivative provided controllability results using Monch's method, Banach's contraction principle, fractional calculus, and semigroup property was studied by the authors Nisar et al [21]. Some recent updates regarding the modeling of the coronavirus, the authors Alderremy et al [23] constructed a mathematical model based on the fuzzy fractional derivative and obtained the results.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of COVID‐19 Using SEIQR Epidemic Model

Avinash

Xavier

Alsinai

et al. 2022

Journal of Mathematics

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The major goal of this study is to create an optimal technique for managing COVID-19 spread by transforming the SEIQR model into a dynamic (multistage) programming problem with continuous and discrete time-varying transmission rates as optimizing variables. We have developed an optimal control problem for a discrete-time, deterministic susceptible class (S), exposed class (E), infected class (I), quarantined class (Q), and recovered class (R) epidemic with a finite time horizon. The problem involves finding the minimum objective function of a controlled process subject to the constraints of limited resources. For our model, we present a new technique based on dynamic programming problem solutions that can be used to minimize infection rate and maximize recovery rate. We developed suitable conditions for obtaining monotonic solutions and proposed a dynamic programming model to obtain optimal transmission rate sequences. We explored the positivity and unique solvability nature of these implicit and explicit time-discrete models. According to our findings, isolating the affected humans can limit the danger of COVID-19 spreading in the future.

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An analysis of controllability results for nonlinear Hilfer neutral fractional derivatives with non-dense domain

Cited by 78 publications

References 27 publications

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

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

Second-grade fluid with Newtonian heating under Caputo fractional derivative: analytical investigations via Laplace transforms

Dynamics of COVID‐19 Using SEIQR Epidemic Model

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