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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]

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]

In this study, we examine the third-order fractional nonlinear Schrödinger equation (FNLSE) in [Formula: see text]-dimensional, by employing the analytical methodology of the new extended direct algebraic method (NEDAM) alongside optical soliton solutions. In order to better understand high-order nonlinear wave behaviors in such systems, the researched model captures the physical and mathematical properties of nonlinear dispersive waves, with applications in plasma physics and optics. With the aid of above mentioned approach, we rigorously assess the novel optical soliton solutions in the form of dark, bright-dark, dark-bright, periodic, singular, rational, mixed trigonometric and hyperbolic forms. Additionally, stability assessments using conserved quantities, such as Hamiltonian property, and consistency checks were used to validate the solutions. The dynamic structure of the governing model is further examined using chaos, bifurcation, and sensitivity analysis. With the appropriate parameter values, 2D, 3D, and contour plots can all be utilized to graphically show the data. This work advances our knowledge of nonlinear wave propagation in Bose-Einstein condensates, ultrafast fibre optics, and plasma physics, among other areas with higher-order chromatic effects., (© 2024. The Author(s).)