On solutions of fractal fractional differential equations

Atangana, Abdon; Akgül, Ali

doi:10.3934/dcdss.2020421

Cited by 25 publications

(27 citation statements)

References 21 publications

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“…It has been shown that fractional-order derivatives have a broad range of applications in the modeling of many chaotic dynamic systems, such as engineering, biology, medicine and many other fields see for example some of the recent results [26] , [21] , [28] , [13] , [33] , [15] . We recall some preliminaries concepts before introducing the proposed fractional epidemic model.…”

Section: Formulation Of the Modelmentioning

confidence: 99%

An epidemic prediction from analysis of a combined HIV-COVID-19 co-infection model via ABC-fractional operator

Ahmed

Goufo

Yusuf

et al. 2021

Alexandria Engineering Journal

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The whole world is still shaken by the new corona virus and many countries are starting opting for the lockdown again after the first wave that already killed thousands of people. New observations also show that the virus spreads quickly during the cold period closer to winter season. On the other side, the number of new infections decreases considerably during hot period closer to summer time. The geographic structure of our planet is such that when some countries (in a hemisphere) are in their winter season, others in the other hemisphere are in their summer season. However, we have observed in the world some countries undertaking national lockdown during their summer time, which result in their economy to be hugely hit. Other factors, beside the lockdown, have also impacted negatively the socio-economic situation in affected countries. These include, among others, the human immunodeficiency virus (HIV) susceptible to combine to the new corona virus. The new corona virus is indeed recent and many of its effect and impact on the society are still unknown and are still to be uncovered. Hence we use here the of Atangana-Baleanu fractional derivative to mathematically express and analyses a model of HIV disease combined with COVID-19 to assess the pandemic situation in many countries affected, such as South Africa, United Kingdom (UK), China, Spain, United States of America (USA), and Italy. A way to achieve that is to perform stability and bifurcation analysis. It is also possible to investigate in which conditions the combined model contains a forward and a backward bifurcation. Moreover, utilizing the techniques of Schaefer and Banach fixed point theorems, existence and uniqueness of solutions of the generalized fractional model were presented. Also, the Atangana-Baleanu fractional (generalized) HIV-COVID-19 con-infection model is solved numerically via well-known and effective numerical scheme and a predicted prevalence for the COVID-19 is provided. The global trend shown by the numerical simulation proves that the disease will stabilize at a later stage when adequate measures are taken.

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Section: Formulation Of the Modelmentioning

confidence: 99%

An epidemic prediction from analysis of a combined HIV-COVID-19 co-infection model via ABC-fractional operator

Ahmed

Goufo

Yusuf

et al. 2021

Alexandria Engineering Journal

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“…There are many kinds of transforms out there in the world. Laplace transform is the most important kind of these transforms [5].…”

Section: Preliminariesmentioning

confidence: 99%

Analysis and new applications of fractal fractional differential equations with power law kernel

Akgül¹

2021

DCDS-S

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We obtain the solutions of fractal fractional differential equations with the power law kernel by reproducing kernel Hilbert space method in this paper. We also apply the Laplace transform to get the exact solutions of the problems. We compare the exact solutions with the approximate solutions. We demonstrate our results by some tables and figures. We prove the efficiency of the proposed technique for fractal fractional differential equations.

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“…Some recent studies on Cutaneous Leishmaniasis epidemic models are described in [6][7][8][9][10][11][12]. Mathematical modeling is one of powerful tools to describe the dynamical behavior of different diseases [13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of five-grade Leishmania epidemic model with harmonic mean-type incidence rate

et al. 2021

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In this paper, we discuss the Anthroponotic Cutaneous Leishmania transmission. In addition, we develop a mathematical model for the Anthroponotic Cutaneous Leishmania transmission and consider its qualitative behavior. We derive the threshold number $R_{0}$ R 0 of the model using the next generation method. In the disease-free case, we carry out the local and global stability under the condition $R_{0}<1$ R 0 < 1 . Moreover, we derive the global stability at the disease-free equilibrium point by utilizing the Castillo-Chavez method. On the other hand, at the endemic equilibrium point, we show the local and global stability to be held under specific conditions and $R_{0}>1$ R 0 > 1 . We also establish the global stability at the endemic equilibrium point with the help of a geometrical approach, which is a generalization of Lyapunov theory, by using a second additive compound matrix. Finally, we take into account the sensitivity analysis of the threshold number with other parameters. We also discuss several graphs of important parameters.

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On solutions of fractal fractional differential equations

Cited by 25 publications

References 21 publications

An epidemic prediction from analysis of a combined HIV-COVID-19 co-infection model via ABC-fractional operator

An epidemic prediction from analysis of a combined HIV-COVID-19 co-infection model via ABC-fractional operator

Analysis and new applications of fractal fractional differential equations with power law kernel

Stability analysis of five-grade Leishmania epidemic model with harmonic mean-type incidence rate

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