Applications of the generalized gamma function to a fractional-order biological system

Matouk, A. E.

doi:10.1016/j.heliyon.2023.e18645

Cited by 7 publications

(4 citation statements)

References 22 publications

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“…Biological systems, including medication administration, bioelectricity, enzyme kinetics, and brain networks, may be effectively modeled using fractional calculus. It aids in capturing the intricate dynamics and enduring memory exhibited in biological systems [3]. Fractional calculus is employed in the development and examination of control systems that exhibit fractional dynamics.…”

Section: Introductionmentioning

confidence: 99%

A Two-Temperature Fractional DPL Thermoelasticity Model with an Exponential Rabotnov Kernel for a Flexible Cylinder with Changeable Properties

Abouelregal,

Alhassan,

Althagafi

et al. 2024

Fractal Fract

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This article presents a new thermoelastic model that incorporates fractional-order derivatives of two-phase heat transfer as well as a two-temperature concept. The objective of this model is to improve comprehension and forecasting of heat transport processes in two-phase-lag systems by employing fractional calculus. This model suggests a new generalized fractional derivative that can make different kinds of singular and non-singular fractional derivatives, depending on the kernels that are used. The non-singular kernels of the normalized sinc function and the Rabotnov fractional–exponential function are used to create the two new fractional derivatives. The thermoelastic responses of a solid cylinder with a restricted surface and exposed to a moving heat flux were examined in order to assess the correctness of the suggested model. It was considered that the cylinder’s thermal characteristics are dependent on the linear temperature change and that it is submerged in a continuous magnetic field. To solve the set of equations controlling the suggested issue, Laplace transforms were used. In addition to the reliance of thermal characteristics on temperature change, the influence of derivatives and fractional order was also studied by providing numerical values for the temperature, displacement, and stress components. This study found that the speed of the heat source and variable properties significantly impact the behavior of the variables under investigation. Meanwhile, the fractional parameter has a slight effect on non-dimensional temperature changes but plays a crucial role in altering the peak value of non-dimensional displacement and pressure.

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Section: Introductionmentioning

confidence: 99%

A Two-Temperature Fractional DPL Thermoelasticity Model with an Exponential Rabotnov Kernel for a Flexible Cylinder with Changeable Properties

Abouelregal,

Alhassan,

Althagafi

et al. 2024

Fractal Fract

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“…In the current century, many engineers, scientists, and economists have described and analyzed their related problems using the aid of fractional calculus (FC) [1][2][3][4][5][6][7][8][9]. The primary rationale is that using FC provides a greater level of accuracy when measuring natural phenomena.…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, FC demonstrated immense potential for applications in various scientific and engineering fields. Notably, it has found utility in disciplines such as engineering [6], fluid dynamics [2], thermoelasticity [4,5], mathematical biology [1,8], as well as market dynamics [9]. Additionally, the biological models that are described in terms of FC involve the memory effect which is considered to be a powerful tool in modeling the epidemiological diseases and viral dynamics.…”

Section: Introductionmentioning

confidence: 99%

“…In Ref. [8], Matouk inserted the extended Gamma function into the CFDO for investigating the complex dynamics in an antimicrobial resistance model. These references [8,27,28] assert that the CFDO involving the extended Gamma function is more suitable to handle the complex dynamics arising from the models that describe the natural phenomena due to its high adequacy in predicting the models' dynamics and also due to the existence of a higher degree of freedom that can be used to obtain more intricate dynamics that cannot present in the case of the corresponding classic fractional Caputo operators.…”

Section: Introductionmentioning

confidence: 99%

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Symmetry in a Fractional-Order Multi-Scroll Chaotic System Using the Extended Caputo Operator

et al. 2023

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In this work, complex dynamics are found in a fractional-order multi-scroll chaotic system based on the extended Gamma function. Firstly, the extended left and right Caputo fractional differential operators are introduced. Then, the basic features of the extended left Caputo fractional differential operator are outlined. The proposed operator is shown to have a new fractional parameter (higher degree of freedom) that increases the system’s ability to display more varieties of complex dynamics than the corresponding case of the Caputo fractional differential operator. Numerical results are performed to show the effectiveness of the proposed fractional operators. Then, rich complex dynamics are obtained such as coexisting one-scroll chaotic attractors, coexisting two-scroll chaotic attractors, or approximate periodic cycles, which are shown to persist in a shorter range as compared with the corresponding states of the integer-order counterpart of the multi-scroll system. The bifurcation diagrams, basin sets of attractions, and Lyapunov spectra are used to confirm the existence of the various scenarios of complex dynamics in the proposed systems.

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Stability and bifurcations in a model of chemostat with two inter‐connected inhibitions and a negative feedback loop

Ben Ali,

Abdellatif

2024

Math Methods in App Sciences

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This paper deals with a model of chemostat with two cross‐feeding species and involving two inhibitions. The excess of hydrogen inhibits the growth of acetogenic bacteria which, in turn, inhibit the growth of methanogenic hydrogenotrophic bacteria. The model is described by a system of four ordinary differential equations. We established the conditions of existence and stability of equilibria with respect to the operating parameters which are the dilution rate and the input substrate concentrations of the species of the model, then we illustrate the operating and bifurcation diagrams. This technique makes it easy to interpret different regions of operating diagrams. Inhibitions let some regions of stability rise and others vanish.

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Applications of the generalized gamma function to a fractional-order biological system

Cited by 7 publications

References 22 publications

A Two-Temperature Fractional DPL Thermoelasticity Model with an Exponential Rabotnov Kernel for a Flexible Cylinder with Changeable Properties

A Two-Temperature Fractional DPL Thermoelasticity Model with an Exponential Rabotnov Kernel for a Flexible Cylinder with Changeable Properties

Symmetry in a Fractional-Order Multi-Scroll Chaotic System Using the Extended Caputo Operator

Stability and bifurcations in a model of chemostat with two inter‐connected inhibitions and a negative feedback loop

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