The role of power decay, exponential decay and Mittag-Leffler function’s waiting time distribution: Application of cancer spread

Atangana, Abdon; Jain, Sonal

doi:10.1016/j.physa.2018.08.033

Cited by 42 publications

(12 citation statements)

References 16 publications

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“…Many approaches, mainly focusing on stochastic arguments, with respect to predicting forecasts of the total number of infected people have appeared during the last weeks [21][22][23][24][25][26] or in the past [27,28]. Recently, neural networks have been applied to forecasting [29] and, additionally, different authors such as Atangana, Baleanu, or Khan have used fractional differential equations in extended SIR-type models to investigate the spread of COVID-19 or mathematical biology in general [30][31][32][33][34].…”

Section: Introduction 1motivationmentioning

confidence: 99%

Time-continuous and time-discrete SIR models revisited: theory and applications

Wacker

Schlüter

2020

Adv Differ Equ

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Since Kermack and McKendrick have introduced their famous epidemiological SIR model in 1927, mathematical epidemiology has grown as an interdisciplinary research discipline including knowledge from biology, computer science, or mathematics. Due to current threatening epidemics such as COVID-19, this interest is continuously rising. As our main goal, we establish an implicit time-discrete SIR (susceptible people–infectious people–recovered people) model. For this purpose, we first introduce its continuous variant with time-varying transmission and recovery rates and, as our first contribution, discuss thoroughly its properties. With respect to these results, we develop different possible time-discrete SIR models, we derive our implicit time-discrete SIR model in contrast to many other works which mainly investigate explicit time-discrete schemes and, as our main contribution, show unique solvability and further desirable properties compared to its continuous version. We thoroughly show that many of the desired properties of the time-continuous case are still valid in the time-discrete implicit case. Especially, we prove an upper error bound for our time-discrete implicit numerical scheme. Finally, we apply our proposed time-discrete SIR model to currently available data regarding the spread of COVID-19 in Germany and Iran.

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Section: Introduction 1motivationmentioning

confidence: 99%

Time-continuous and time-discrete SIR models revisited: theory and applications

Wacker

Schlüter

2020

Adv Differ Equ

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“…However, this apparent limitation allows to describe more appropriate real world problems. () Atangana and Gómez proposed the work entitled “Decolonization of fractional calculus rules: breaking commutativity and associativity to capture more natural phenomena.” In this work, several examples of noncommutative and nonassociative problems were presented. Also, the authors justify why the fractional derivatives with nonsingular kernel are needed to describe those physical problems.…”

Section: Resultsmentioning

confidence: 99%

Determination of supercapacitor parameters based on fractional differential equations

Hidalgo‐Reyes

Gómez‐Aguilar

Escobar-Jiménez

et al. 2019

Circuit Theory & Apps

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In this paper, we estimate the parameter values of a fractional-order model of supercapacitors involving fractional derivatives of Liouville-Caputo, Caputo-Fabrizio, and Atangana-Baleanu and fractional conformable derivative in the Liouville-Caputo sense. We present the exact solution of the considered model using the properties of the Laplace transform operator together with the convolution theorem. They developed numerical simulations using each one of the fractional derivatives; the results were compared graphically with experimental data obtained from different supercapacitors using standard laboratory equipment. The nonlocal parameters involved in the equivalent electrical circuit for the supercapacitor model are recalculated for each fractional derivative using a particle swarm optimization algorithm for generating optimal solutions. KEYWORDS exponential decay-law, fractional calculus, fractional conformable derivative, Mittag-Leffler function, power-law, supercapacitor model Int J Circ Theor Appl. 2019;47:1225-1253.wileyonlinelibrary.com/journal/cta

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“…In this section, we obtain alternative representations of the cancer model considering the Caputo-Fabrizio and Atangana-Baleanu fractional derivatives, for the discretization of fractional model equations by Adams-Bashforth method [2,3] .…”

Section: Covid-19 Model With Fractional Derivativementioning

confidence: 99%

A novel mathematics model of covid-19 with fractional derivative. Stability and numerical analysis

Alkahtani

2020

Chaos, Solitons & Fractals

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Elsevier has created a COVID-19 resource centre with free information in English and Mandarin on the novel coronavirus COVID-19. The COVID-19 resource centre is hosted on Elsevier Connect, the company's public news and information website. Elsevier hereby grants permission to make all its COVID-19-related research that is available on the COVID-19 resource centre-including this research content-immediately available in PubMed Central and other publicly funded repositories, such as the WHO COVID database with rights for unrestricted research re-use and analyses in any form or by any means with acknowledgement of the original source. These permissions are granted for free by Elsevier for as long as the COVID-19 resource centre remains active.

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The role of power decay, exponential decay and Mittag-Leffler function’s waiting time distribution: Application of cancer spread

Cited by 42 publications

References 16 publications

Time-continuous and time-discrete SIR models revisited: theory and applications

Time-continuous and time-discrete SIR models revisited: theory and applications

Determination of supercapacitor parameters based on fractional differential equations

A novel mathematics model of covid-19 with fractional derivative. Stability and numerical analysis

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