Dynamics of Fractional Chaotic Systems with Chebyshev Spectral Approximation Method

Owolabi, Kolade M.; Pindza, Edson

doi:10.1007/s40819-022-01340-2

Cited by 5 publications

(2 citation statements)

References 45 publications

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“…The fact that the fractal fractional derivative provides the opportunity to examine the fractal dimension while evaluating the real phenomena in terms of fractional has enabled many researchers to concentrate on this subject. Many studies valuable papers, books, and scientific reports have been carried out with the concepts of fractional and fractal derivatives and they can be found there and in the references therein [ 15 , 18 , 25 , 38 , 57 ].…”

Section: The Diabetes Mellitus Modelmentioning

confidence: 99%

A computational technique for the Caputo fractal-fractional diabetes mellitus model without genetic factors

Karaağaç

Owolabi

Pindza

2023

Int. J. Dynam. Control

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The concept of a Caputo fractal-fractional derivative is a new class of non-integer order derivative with a power-law kernel that has many applications in real-life scenarios. This new derivative is applied newly to model the dynamics of diabetes mellitus disease because the operator can be applied to formulate some models which describe the dynamics with memory effects. Diabetes mellitus as one of the leading diseases of our century is a type of disease that is widely observed worldwide and takes the first place in the evolution of many fatal diseases. Diabetes is tagged as a chronic, metabolic disease signalized by elevated levels of blood glucose (or blood sugar), which results over time in serious damage to the heart, blood vessels, eyes, kidneys, and nerves in the body. The present study is devoted to mathematical modeling and analysis of the diabetes mellitus model without genetic factors in the sense of fractional-fractal derivative. At first, the critical points of the diabetes mellitus model are investigated; then Picard’s theorem idea is applied to investigate the existence and uniqueness of the solutions of the model under the fractional-fractal operator. The resulting discretized system of fractal-fractional differential equations is integrated in time with the MATLAB inbuilt Ode45 and Ode15s packages. A step-by-step and easy-to-adapt MATLAB algorithm is also provided for scholars to reproduce. Simulation experiments that revealed the dynamic behavior of the model for different instances of fractal-fractional parameters in the sense of the Caputo operator are displayed in the table and figures. It was observed in the numerical experiments that a decrease in both fractal dimensions and leads to an increase in the number of people living with diabetes mellitus.

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Section: The Diabetes Mellitus Modelmentioning

confidence: 99%

A computational technique for the Caputo fractal-fractional diabetes mellitus model without genetic factors

Karaağaç

Owolabi

Pindza

2023

Int. J. Dynam. Control

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“…Among these three definitions, the Caputo FD definition is most popular among physicists, engineers and researchers. Fractional derivative definition in the Caputo sense has been used for capturing FO dynamics in many real-world systems like predator–prey system [ 33 , 34 ], chaotic systems and maps [ 35 – 37 ], COVID-19 pandemic [ 38 ], symbiosis dynamics [ 39 ], biological systems [ 40 ], physics [ 41 ], engineering systems [ 42 ], nuclear reactor [ 43 ], anomalous diffusion [ 44 ], superdiffusive system [ 45 ], cancer [ 46 ], renewable energy systems [ 47 ], to name a few. This work also employs Caputo fractional derivative definition in all the FDE models.…”

Section: Fractional Calculusmentioning

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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Analysis of the muzzle dynamic response interval based on the bond space method

He,

Dai,

Lin

et al. 2023

J Mech Sci Technol

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Dynamics of Fractional Chaotic Systems with Chebyshev Spectral Approximation Method

Cited by 5 publications

References 45 publications

A computational technique for the Caputo fractal-fractional diabetes mellitus model without genetic factors

A computational technique for the Caputo fractal-fractional diabetes mellitus model without genetic factors

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

Analysis of the muzzle dynamic response interval based on the bond space method

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