The objective of this manuscript is to present a novel approach to modeling influenza A disease dynamics by incorporating the Caputo-Fabrizio (CF) fractional derivative operator into the model. Particularly distinct contact rates between exposed and infected individuals are taken into account in the model under study, and the fractional derivative concept is explored with respect to this component. We demonstrate the existence and uniqueness of the solution and obtain the series solution for all compartments using the Laplace transform method. The reproduction number of the Influenza A model, which was created to show the effectiveness of different contact rates, was obtained and examined in detail in this sense. To validate our approach, we applied the predictor-corrector method in the sense of the Caputo-Fabrizio fractional derivative and demonstrate the effectiveness of the fractional derivative in accurately predicting disease dynamics. Our findings suggest that the use of the Caputo-Fabrizio fractional derivative can provide valuable insights into the mechanisms underlying influenza A disease and enhance the accuracy of disease models.

It is possible to produce mobile phone worms, which are computer viruses with the ability to command the running of cell phones by taking advantage of their flaws, to be transmitted from one device to the other with increasing numbers. In our day, one of the services to gain currency for circulating these malignant worms is SMS. The distinctions of computers from mobile devices render the existing propagation models of computer worms unable to start operating instantaneously in the mobile network, and this is particularly valid for the SMS framework. The susceptible–affected–infectious–suspended–recovered model with a classical derivative (abbreviated as SAIDR) was coined by Xiao et al., (2017) in order to correctly estimate the spread of worms by means of SMS. This study is the first to implement an Atangana–Baleanu (AB) derivative in association with the fractional SAIDR model, depending upon the SAIDR model. The existence and uniqueness of the drinking model solutions together with the stability analysis are shown through the Banach fixed point theorem. The special solution of the model is investigated using the Laplace transformation and then we present a set of numeric graphics by varying the fractional-order $\theta$ with the intention of showing the effectiveness of the fractional derivative.

This paper deals with implementation of the multistage Adomian decomposition method (MADM) to solve a class of nonlinear programming (NLP) problems, which are reformulated with a nonlinear system of fractional differential equations. The multistage strategy is used to investigate the relation between an equilibrium point of the fractional order dynamical system and an optimal solution of the NLP problem. The preference of the method lies in the fact that the multistage strategy gives this relation in an arbitrary longtime interval, while the Adomian decomposition method (ADM) gives the optimal solution just only in the neighborhood of the initial time. The numerical results taken by the fractional order MADM show that these results are compatible with the solution of NLP problem rather than the ADM. Furthermore, in some cases the fractional order MADM can perform more rapid convergency to the optimal solution of optimization problem than the integer order ones.

Infectious diseases have caused the death of many people throughout the world for centuries. For this purpose, many researchers have investigated these diseases for establishing new treatment and protective measures. The most important of these is HIV disease. In this study, an HIV infection model of CD 4 ⁺ T cells is handled comprehensively with the newly defined Atangana-Baleanu (AB) fractional derivative. The existence and uniqueness of the solutions for fractionalized HIV disease model with the new derivative by considering the Arzela-Ascoli theorem.

Smoking is the most lethal social poisoning event. The World Health Organization defines smoking as the most important preventable cause of disease. Around 4.9 million people worldwide die from smoking every year. In order to analysis this matter, we aim to investigate an e-cigarette smoking model with Atangana-Baleanu fractional derivative. We obtain the existence conditions of the solution for this fractional model utilizing fixed-point theory. After giving existence conditions, the uniqueness of the solution is proved. Finally, to show the effect of the Atangana-Baleanu fractional derivative on the model, we give some numerical results supported by illustrative graphics.