Analysis of solitary wave solutions in the fractional-order Kundu-Eckhaus system.

The area of fractional partial differential equations has recently become prominent for its ability to accurately simulate complex physical events. The search for traveling wave solutions for fractional partial differential equations is a difficult task, which has led to the creation of numerous mathematical approaches to tackle this problem. The primary objective of this research work is to provide optical soliton solutions for the Frictional Kundu-Eckhaus equation (FKEe) by utilizing generalized coefficients. This strategy utilizes the Riccati-Bernoulli sub-ODE technique to effectively discover the most favorable traveling wave solutions for fractional partial differential equations. As a result, it facilitates the extraction of optical solitons and intricate wave solutions. The Backlund transformation is used to methodically construct a sequence of solutions for the specified equations. The study additionally showcases 3D and Density graphics that visually depict chosen solutions for certain parameter selections, hence improving the understanding of the outcomes.

A novel discrete-time COVID-19 epidemic model including the compartment of vaccinated individuals.

Referring tothe study of epidemic mathematical models, this manuscript presents a noveldiscrete-time COVID-19 model that includes the number of vaccinated individuals as an additional state variable in the system equations. The paper shows that the proposed compartment model, described by difference equations, has two fixed points, i.e., a disease-free fixed point and an epidemic fixed point. By considering both the forward difference system and the backward difference system, some stability analyses of the disease-free fixed point are carried out.In particular, for the backward difference system a novel theorem is proved, which gives a condition for the disappearance of the pandemic when an inequality involving some epidemic parameters is satisfied. Finally, simulation results of the conceived discrete model are carried out, along with comparisons regarding the performances of both the forward difference system and the backward difference system.

Dynamical Analysis of a New Chaotic Fractional Discrete-Time System and Its Control.

This article proposes a new fractional-order discrete-time chaotic system, without equilibria, included two quadratic nonlinearities terms. The dynamics of this system were experimentally investigated via bifurcation diagrams and largest Lyapunov exponent. Besides, some chaotic tests such as the 0-1 test and approximate entropy (ApEn) were included to detect the performance of our numerical results. Furthermore, a valid control method of stabilization is introduced to regulate the proposed system in such a way as to force all its states to adaptively tend toward the equilibrium point at zero. All theoretical findings in this work have been verified numerically using MATLAB software package.