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In this article, a diffusion component in an SIR model is introduced, and its impact is analyzed using fractional calculus. We have included the diffusion component in the SIR model. in order to illustrate the variations. Here, we have applied the general fractional derivative to analyze the impact. The Laplace decomposition technique is employed to obtain the numerical outcomes of the model. In order to observe the effect of the diffusion component in the SIR model, graphical solutions are also displayed. [ABSTRACT FROM AUTHOR]

A five-dimensional hyperchaotic system is a dynamical system with five state variables that exhibits chaotic behavior in multiple directions. In this work, we incorporated a 5D hyperchaotic system with constant- and variable-order Caputo and the Caputo–Fabrizio fractional derivatives. These fractional 5D hyperchaotic systems are solved numerically. Through simulations, the chaotic behavior of these fractional-order hyperchaotic systems is analyzed and a comparison between constant- and variable-order fractional hyperchaotic systems is presented. [ABSTRACT FROM AUTHOR]

In the context of fractal space, this study presents a higher-order nonlinear local fractional Bratu-type equation and thoroughly examines this generalized nonlinear equation. Additional analysis and identification of particular special situations of the generalized local fractional Bratu equation is performed. Finally, the Adomian decomposition method is utilized to derive that solution for the generalized Bratu equation of local fractional type. This study contributes to a deeper understanding of these equations and provides a practical computational approach to their solutions. [ABSTRACT FROM AUTHOR]

In this study we have proposed the SIAQR model with time-dependent infection rate. The model's well-posedness is demonstrated, and the proposed model is then extended to the fractional mathematical model by employing the Caputo-Fabrizio fractional derivative operator. We have also used the Lipschitz condition and the linear growth condition to determine the conditions under which the model has a unique solution. The numerical solutions are presented. Furthermore, using graphical representations we will see how the number of infected, recovered individuals vary as the order of fractional derivative varies. [ABSTRACT FROM AUTHOR]

In this paper, a new fractional derivative operator is introduced with the help of Lonezo–Hartely function (G‐function). Further, with the help of this fractional derivative operator, a new fractional diffusion equation is proposed and solved analytically with the help of Laplace transform. Some applications related to the operator are also discussed in corollaries. [ABSTRACT FROM AUTHOR]

In our research work, we suggest the modified minimal model of fractional order and analyze it using the homotopy decomposition method (HDM). The minimal model is quite a useful mathematical model which describes the behavior of glucose-insulin metabolism. The original model was given in the 80s and has been updated over a different period. In this modified model, we add a one-factor diet which plays an important role in the blood-glucose analysis. We obtained the numerical results by using the homotopy decomposition method. HDM is extremely useful, significant, and very simple. We also discuss the existence and uniqueness of the fractional model. [ABSTRACT FROM AUTHOR]

In this paper, we solve the local fractional generalized Fokker–Planck equation. To solve the problem, local fractional Mohand transform with Adomian decomposition method is introduced due to its simple approach and less computational work. Furthermore, for the applicability of the technique, we illustrate some examples and their exact or approximate solutions with their graphical representations. [ABSTRACT FROM AUTHOR]

Diabetes is a burning issue in the whole world. It is the imbalance between body glucose and insulin. The study of this imbalance is very much needed from a research point of view. For this reason, Bergman gave an important model named-Bergman minimal model. In the present work, using Caputo-Fabrizio (CF) fractional derivative, we generalize Bergman's minimal blood glucose-insulin model. Further, we modify the old model by including one more component known as diet D(t), which is also essential for the blood glucose model. We solve the modified model with the help of Sumudu transform and fixed-point iteration procedures. Also, using the fixed point theorem, we examine the existence and uniqueness of the results along with their numerical and graphical representation. Furthermore, the comparison between the values of parameters obtained by calculating different values of t with experimental data is also studied. Finally, we draw the graphs of G(t), X(t), I(t), and D(t) for different values of τ. It is also clear from the obtained results and their graphical representation that the obtained results of modified Bergman's minimal model are better than Bergman's model. [ABSTRACT FROM AUTHOR]

We introduced the fading memory effect to the model portraying the prediction in physical condition. The classical model is known as the Banister model. We presented the existence and uniqueness conditions of the exact solutions of this model using three different memory including the bad memory induces by the power law and the good memories induced by exponential decay law and the Mittag-Leffler law. We derived the exact solutions using the Laplace transform for the non-delay version. [ABSTRACT FROM AUTHOR]

In the present paper, we use an efficient approach to solve fractional differential equation, oxygen diffusion problem which is used to describe oxygen absorption in human body. The oxygen diffusion problem is considered in new Caputo derivative of fractional order in this paper. Using an iterative approach, we derive the solutions of the modified system. [ABSTRACT FROM AUTHOR]