Fractional-order Modeling of Nuclear Reactor: From Subdiffusive Neutron Transport to Control-oriented Models

Vyawahare, Vishwesh A.; Nataraj, P. S. V.

doi:10.1007/978-981-10-7587-2

Cited by 21 publications

(11 citation statements)

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“…In the past two decades, there has been tremendous interest in studying fractional differential equations (FDEs for short) due to their extensive applications in various fields of engineering and scientific disciplines (see [1][2][3][4][5][6][7][8]). For example, in [8], Laskin proposed the following fractional stochastic dynamic model for the considered market:…”

Section: Introductionmentioning

confidence: 99%

Existence and uniqueness results for the coupled systems of implicit fractional differential equations with periodic boundary conditions

2018

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Section: Introductionmentioning

confidence: 99%

Existence and uniqueness results for the coupled systems of implicit fractional differential equations with periodic boundary conditions

2018

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“…The FO neutron diffusion equation models were proposed in [ 7 , 8 , 49 ]. The FO models used in the work are proposed in [ 5 ]. These models are based on the assumption that the neutron transport inside the reactor core should be modeled as subdiffusion and were derived for slab geometry.…”

Section: Fractional-order Models Of Nuclear Reactormentioning

confidence: 99%

“…Recent years have seen the successful application of fractional differential equations (FDEs) for modeling nuclear reactors which includes formulation, derivation and a detailed study of fractional-order (FO) neutron transport equation, FO telegraph models, FO diffusion models, FO point reactor kinetics model, FO 2-group models and other FO models. Refer [ 5 ] for a detailed survey on FO nuclear rector models.…”

Section: Introductionmentioning

confidence: 99%

Modeling nonlinear fractional-order subdiffusive dynamics in nuclear reactor with artificial neural networks

Bhusari¹,

Patil²,

Jadhav³

et al. 2022

Int. J. Dynam. Control

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This paper presents the development and analysis of artificial neural network (ANN) models for the nonlinear fractional-order (FO) point reactor kinetics model, FO Nordheim–Fuchs model, inverse FO point reactor kinetics model and FO constant delayed neutron production rate approximation model. These models represent the dynamics of a nuclear reactor with neutron transport modeled as subdiffusion. These FO models are nonlinear in nature, are comprised of a system of coupled fractional differential equations and integral equations, and are considered to be difficult for solving both analytically and numerically. The ANN models were developed using the data generated from these models. The work involves the iterative process of ANN learning with different combinations of layers and neurons. It is shown through extensive simulation studies that the developed ANN models faithfully capture the transient and steady-state dynamics of these FO models, thereby providing a satisfactory representation for the nonlinear subdiffusive process of neutron transport in a nuclear reactor.

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“…The previous studies review that fractional calculus provides more exact models of several applications and shows the behaviour of the dynamic system in sciences than traditional calculus [7,8,9,10]. A system of non-linear fractional-order reaction-diffusion equations was used to model the superdiffusive spread of modern epidemics because compared with integer-order is well capable of capturing the memory-like effect examined in the non-linear dynamic system [11]. Other recent study includes a fractional -order Brusselator reaction-diffusion model in a triple collision and enzymatic reactions system [12], fractionalorder mathematical modeling of novel corona virus (COVID-19) [13], and fractional-order analytical and qualitative investigation of (COVID-19) mathematical model [14].…”

Section: Iintroductionmentioning

confidence: 99%

Efficient Solution of Fractional-Order SIR Epidemic Model of Childhood Diseases With Optimal Homotopy Asymptotic Method

2022

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In providing an accurate approximate analytical solution to the non-linear system of fractional-order susceptible-infected-recovered epidemic model (FOSIREM) of childhood disease has been a challenge because no norm guarantees the convergence of the infinite series solution. We compute an accurate approximate analytical solution using the optimal homotopy asymptotic method (OHAM). The fractional differential equations operator (FDEO) is given as conformable derivative operator (CDO). We show the basic idea of the proposed method, the CDO sense, equilibrium points, local asymptotic stability, reproduction number, and the convergence analysis of the proposed method. Numerical results and comparisons with other approximate analytical solutions are given to validate the efficiency of the method. The proposed method speedily converges to the exact solution as the fractional-order derivative approaches 1 proved an excellent tool for solving and predicting the model.

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Fractional-order Modeling of Nuclear Reactor: From Subdiffusive Neutron Transport to Control-oriented Models

Cited by 21 publications

References 0 publications

Existence and uniqueness results for the coupled systems of implicit fractional differential equations with periodic boundary conditions

Existence and uniqueness results for the coupled systems of implicit fractional differential equations with periodic boundary conditions

Modeling nonlinear fractional-order subdiffusive dynamics in nuclear reactor with artificial neural networks

Efficient Solution of Fractional-Order SIR Epidemic Model of Childhood Diseases With Optimal Homotopy Asymptotic Method

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