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In this present paper, we investigate a new model for fluids in the context of fractional calculus. We study the fractional diffusion reaction equations. In our model, the reaction term describes a fractional heat equation. We present the qualitative properties of the introduced models. We propose the solution of the fractional diffusion reaction equations represented by the Caputo-Liouville generalized fractional derivative. We combine in this work the Laplace transformation and the Fourier transformation for getting the solutions of the introduced models. Our contributions are to analyze the impact of the fractional-order derivative and the reaction term on the diffusion processes. We also interpret the effect of the Prandtl number P r on the diffusion processes. [ABSTRACT FROM AUTHOR]

This paper aims to study the stability of the fractional differential equations without inputs. The fractional differential equations without inputs considered in this paper are defined with the Caputo-Fabrizio fractional derivative operator. We will investigate to find the stability conditions related to the fractional differential equations. We will address how to characterize the stability of fractional differential equations using the Lyapunov candidates' functions. The stability conditions of the perturbed fractional differential equations will be discussed. The Lyapunov characterization of the stability will be proposed to avoid the difficulty existing when we analyze stability using the Gronwall lemma and the trajectories analysis. Several examples to illustrate the mains results will be provided. [ABSTRACT FROM AUTHOR]

In recent years, there are many new definitions that were proposed related to fractional derivatives, and with the help of these definitions, mathematical models were established to overcome the various real-life problems. The true purpose of the current work is to develop and analyze Atangana-Baleanu (AB) with Mittag-Leffler kernel and Atangana-Toufik method (ATM) of fractional derivative model for the Smoking epidemic. Qualitative analysis has been made to `verify the steady state. Stability analysis has been made using self-mapping and Banach space as well as fractional system is analyzed locally and globally by using first derivative of Lyapunov. Also derive a unique solution for fractional-order model which is a new approach for such type of biological models. A few numerical simulations are done by using the given method of fractional order to explain and support the theoretical results., Competing Interests: The authors state that there is no conflict of interest., (Copyright © 2022 Aqeel Ahmad et al.)

In this manuscript, we investigate the approximate solutions to the tangent nonlinear packaging equation in the context of fractional calculus. It is an important equation because shock and vibrations are unavoidable circumstances for the packaged goods during transport from production plants to the consumer. We consider the fractal fractional Caputo operator and Atangana-Baleanu fractal fractional operator with nonsingular kernel to obtain the numerical consequences. Both fractal fractional techniques are equally good, but the Atangana-Baleanu Caputo method has an edge over Caputo method. For illustrations and clarity of our main results, we provided the numerical simulations of the approximate solutions and their physical interpretations. This paper contributes to the new applications of fractional calculus in packaging systems., (© Islamic Azad University 2021.)

In this work, we develop and analyze a mathematical model for the dynamics of COVID-19 with re-infection in order to assess the impact of prior comorbidity (specifically, diabetes mellitus ) on COVID-19 complications. The model is simulated using data relevant to the dynamics of the diseases in Lagos, Nigeria, making predictions for the attainment of peak periods in the presence or absence of comorbidity. The model is shown to undergo the phenomenon of backward bifurcation caused by the parameter accounting for increased susceptibility to COVID-19 infection by comorbid susceptibles as well as the rate of reinfection by those who have recovered from a previous COVID-19 infection. Simulations of the cumulative number of active cases (including those with comorbidity), at different reinfection rates, show infection peaks reducing with decreasing reinfection of those who have recovered from a previous COVID-19 infection. In addition, optimal control and cost-effectiveness analysis of the model reveal that the strategy that prevents COVID-19 infection by comorbid susceptibles is the most cost-effective of all the control strategies for the prevention of COVID-19., Competing Interests: The authors declare that they have no conflict of interests., (© 2021 John Wiley & Sons Ltd.)

In this paper, we propose a mathematical model to predict the novel coronavirus. Due to the rapid spread of the novel coronavirus disease in the world, we add to the deterministic model of the coronavirus the terms of the stochastic perturbations. In other words, we consider in this paper a stochastic model to predict the novel coronavirus. The equilibrium points of the deterministic model have been determined, and the reproduction number of our deterministic model has been implemented. The asymptotic behaviors of the solutions of the stochastic model around the equilibrium points have been studied. The numerical investigations and the graphical representations obtained with the novel stochastic model are made using the classical stochastic numerical scheme., Competing Interests: Competing interestsThe author declares that they have no competing interests., (© The Author(s) 2020.)

Analytical solutions of the first and second model of Hristov fractional diffusion equations based on the non-singular Atangana-Baleanu derivative have been developed. The solutions are based on an integral method based on the consequent application of the Fourier and Laplace transforms. Particular cases of Hristov fractional diffusion equations considering operators with orders converging to unity have been analyzed, too.

The Government of Senegal, in keeping with the priority given to women and children in its health programs, requested the assistance of the United Nations Development Program (UNDP) in identifying and executing a program to diminish maternal mortality in that country. A UNDP "Mission of Identification" was carried out in response to this initiative. The preliminary results of this mission confirm that the issue of maternal safety is of primary concern not only to the government but also to women in the Republic of Senegal. The methodology employed during this mission allowed the team of national and international experts to confirm the level of this concern and to identify four major potential areas of intervention. Quantitative goals for the program have been set and estimates for the efficacy of each of the intervention areas indicate that intervention through the timely provision of access to emergency surgical services and appropriate prenatal care will yield the largest reduction. The feasibility of providing interventions in each of the four areas was also addressed during the mission. This methodology will be applicable to other settings as Third World countries begin to address the problem of excessive maternal mortality.