Analysis and Dynamics of Illicit Drug Use Described by Fractional Derivative with Mittag-Leffler Kernel

Karaağaç, Berat; Owolabi, Kolade M.; Nisar, Kottakkaran Sooppy

doi:10.32604/cmc.2020.011623

Cited by 31 publications

(11 citation statements)

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“…At the same time, the paper builds the principle model of the higher vocational students' psychological information system. The specific steps are detailed as follows: y represents the characteristic variables of the psychological and physiological outstanding performance of vocational students [4]. The characteristic variable of the mental state of vocational students is 1 2 ( , , , )…”

Section: The Principle Model Of Higher Vocational Students' Psycholog...mentioning

confidence: 99%

The Mental Health Education Management of Higher Vocational Students Based on Fractional Differential Equations

Zhang

2022

Applied Mathematics and Nonlinear Sciences

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Based on fractional differential equations, this paper proposes an optimization modeling method for the mental health quality of vocational students. This article quantifies the psychology of higher vocational students from the perspective of fractional differential equations. At the same time, we use alertness to characterize the risk of mental fatigue and propose a mental health energy equation. We propose a mental health energy replenishment function and consumption function and describe mental health energy during sleep. Finally, we use fractional differential equations to reason about the model deductively. The research shows that it is feasible for us to apply fractional differential equations to predict the mental health problems of vocational students.

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Section: The Principle Model Of Higher Vocational Students' Psycholog...mentioning

confidence: 99%

The Mental Health Education Management of Higher Vocational Students Based on Fractional Differential Equations

Zhang

2022

Applied Mathematics and Nonlinear Sciences

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“…The RKHA has many motivational aspects and a great ability to handle complicated problems without imposing any restrictions on the style of the models. Therefore, it has been gaining a lot of solicitude and examination lately [24][25][26][27][28][29][30][31][32].…”

Section: Reproducing Kernel: Preliminaries and Definitionsmentioning

confidence: 99%

Hilbert solution, iterative algorithms, convergence theoretical results, and error bound for the fractional Langevin model arising in fluids with Caputo’s independent derivative

2022

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Studying and analyzing the random motion of a particle immersed in a liquid represented in the Langevin fractional model by Caputo’s independent derivative is one of the aims of applied physics. In this article, we will attend to a new, accurate, and comprehensive numerical solution to the aforementioned model using the reproducing kernel Hilbert approach. Basically, numerical and exact solutions of the fractional Langevin model are represented using an infinite/finite sum, simultaneously, in the Σ2Ξ space. The proof has been sketched for many mathematical theorems such as independence, convergence, error behavior, and completeness of the solution. A sufficient set of tabular results and two-dimensional graphs are shown, and absolute/relative error graphs that express the dynamic behavior of the fractional parameters α,β are utilized as well. From an analytical and practical point of view, we noticed that the simulation process and the iterative approach are appropriate, easy, and highly efficient tools for solving the studied model. In conclusion, what we have carried out is presented with a set of recommendations and an outlook on the most important literature used.

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“…Over the last decades, the use of fractional calculus has rapidly increased in many areas of science and engineering [1][2][3][4]. Fractional calculus is a generalization of the standard integer-order calculus and it brings more degrees of freedom for differentiation in the modeling of various phenomena that are encountered in many application areas, such as biology [5,6], engineering and various domains of applied sciences [7,8].…”

Section: Introductionmentioning

confidence: 99%

Three-Species Lotka-Volterra Model with Respect to Caputo and Caputo-Fabrizio Fractional Operators

et al. 2021

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In this paper, we apply the concept of fractional calculus to study three-dimensional Lotka-Volterra differential equations. We incorporate the Caputo-Fabrizio fractional derivative into this model and investigate the existence of a solution. We discuss the uniqueness of the solution and determine under what conditions the model offers a unique solution. We prove the stability of the nonlinear model and analyse the properties, considering the non-singular kernel of the Caputo-Fabrizio operator. We compare the stability conditions of this system with respect to the Caputo-Fabrizio operator and the Caputo fractional derivative. In addition, we derive a new numerical method based on the Adams-Bashforth scheme. We show that the type of differential operators and the value of orders significantly influence the stability of the Lotka-Volterra system and numerical results demonstrate that different fractional operator derivatives of the nonlinear population model lead to different dynamical behaviors.

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Analysis and Dynamics of Illicit Drug Use Described by Fractional Derivative with Mittag-Leffler Kernel

Cited by 31 publications

References 0 publications

The Mental Health Education Management of Higher Vocational Students Based on Fractional Differential Equations

The Mental Health Education Management of Higher Vocational Students Based on Fractional Differential Equations

Hilbert solution, iterative algorithms, convergence theoretical results, and error bound for the fractional Langevin model arising in fluids with Caputo’s independent derivative

Three-Species Lotka-Volterra Model with Respect to Caputo and Caputo-Fabrizio Fractional Operators

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