Mathematical assessment of the dynamics of the tobacco smoking model: An application of fractional theory

Liu, Yijie; Munir, Taj; Cui, Ting; Din, Anwarud; Wu, Peng

doi:10.3934/math.2022398

Cited by 17 publications

(5 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…FDEs are global in nature, more realistic, and give great degree of freedom to modelers as compared to the CDEs. Modeling via FDEs has produced highly influential results in the investigation of transmission of the infectious diseases models [23,24].…”

Section: Introductionmentioning

confidence: 99%

[Retracted] The Mathematical Analysis of the New Fractional Order Ebola Model

Khan

Ali

Bonyah³

et al. 2022

Journal of Nanomaterials

View full text Add to dashboard Cite

This research study focuses on the analytical behavior and numerical computation of the fractional order Ebola model. In this study we have calculated the conditions for the existence, uniqueness, and stability of the solution with the help of the fixed point results. In addition to this, we calculated the numerical solution of the fractional order smoke model with the help two-step fractional Adam’s Bashforth method using the Caputo’s fractional derivative of order μ . Furthermore, the results obtained for different orders of the fractional derivative μ have been shown graphically with the help of Matlab.

show abstract

Section: Introductionmentioning

confidence: 99%

[Retracted] The Mathematical Analysis of the New Fractional Order Ebola Model

Khan

Ali

Bonyah³

et al. 2022

Journal of Nanomaterials

View full text Add to dashboard Cite

show abstract

“…By following the idea reported in [50] , [54] , [62] , we consider the Cauchy problem associated with the CFD given as

The Cauchy problem (21) is transformed by using the Caputo integral

At the point

and

with

being the time step, Eq. (22) is formulated as

which can be written as

Using the Lagrange polynomial [19] , [20] , [33] , [54] , and simplifying the integral on the right side, Eq. (24) is changed into Eq.…”

Section: Numerical Schemementioning

confidence: 99%

“…Mathematical models based on ordinary differential equations of integer order have been widely employed to study the dynamics of biological systems [17] , [18] . Based on the principles of mathematical epidemiology, a number of mathematical models for social epidemics (such as crime and drug abuse) has also been presented [19] , [20] , [21] , [22] . Every model is based on classical derivatives, with different constraints depending on the differential equation order.…”

Section: Introductionmentioning

confidence: 99%

A new fractional mathematical model to study the impact of vaccination on COVID-19 outbreaks

Kumawat

Bhatter

Jangid

et al. 2023

Decision Analytics Journal

View full text Add to dashboard Cite

“…(2) Definition 3. [89] The corresponding integral operator of fractional order α ∈ [0, 1] is defined:…”

Section: Definition 2[89]mentioning

confidence: 99%

Untitled

2023

Progr. Fract. Differ. Appl.

View full text Add to dashboard Cite

Both mathematics and science are important for one another and have a close relationship. It is impossible to dispute the significance of mathematics in a number of scientific disciplines, including electrical engineering, physics, biology, and medicine. Due to a number of applications of mathematical biology in the twenty-first century, researchers have taken a special interest in this field. Due to the complexity of the underlying connections, both deterministic and stochastic epidemiological models are founded on an inadequate understanding of the infectious network. Over the past several years, the use of different fractional operators to model the problem has grown, and it is now a common way to study how epidemics spread. New fractional operators, the infectious disease model has been studied in this paper. By using different numerical techniques and the time fractional parameters, the mechanical characteristics of the fractional order model are identified. The uniqueness and existence have been established. The model's local and global stability analysis has been found. In order to justify the theoretical results, numerical simulations are carried out for the presented method in the range of fractional order to show the implications of fractional and fractal orders. We applied very effective numerical technique to obtain the solutions of the model and simulations. Also, we present conditions of existence for a solution to the purposed epidemic model and to calculate the reproduction number in certain state conditions of the analyzed dynamic system. Infectious disease fractional order model is offered for analysis with simulations in order to determine the possible efficacy of disease transmission in the Community. The Fractal fractional operator is employed to study the dynamical transmission of diseases effect on society which is helpful for analysis, decision making, and disease control. Are treated with the Banach contraction principle. Microorganisms, interactions between individuals or groups, and environmental, social, economic, and demographic factors on a broader scale are all examples. Finally, numerical simulations that demonstrate the impact of fractional parameters on our found solutions are built to study the impact of the system parameter on the disease's spread. In conclusion, fractional operators in mathematical models can help decision-makers make better choices regarding the course of action to take in an epidemic situation. Further, we suggested some future work directions with the help of the new hybrid fractional operator. Fractional Calculus is a prominent topic for research within the discipline of Applied Mathematics due to its usefulness in solving problems in many different branches of science, engineering, and medicine. Recent researchers have identified the importance of mathematical tools in various disease models as being very useful to study the dynamics with the help of fractional and integer calculus modeling.

show abstract

Mathematical assessment of the dynamics of the tobacco smoking model: An application of fractional theory

Cited by 17 publications

References 35 publications

[Retracted] The Mathematical Analysis of the New Fractional Order Ebola Model

[Retracted] The Mathematical Analysis of the New Fractional Order Ebola Model

A new fractional mathematical model to study the impact of vaccination on COVID-19 outbreaks

Untitled

Contact Info

Product

Resources

About