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New fractional operators, the COVID-19 model has been studied in this paper. By using different numerical techniques and the time fractional parameters, the mechanical characteristics of the fractional order model are identified. The uniqueness and existence have been established. The model's Ulam-Hyers stability analysis has been found. In order to justify the theoretical results, numerical simulations are carried out for the presented method in the range of fractional order to show the implications of fractional and fractal orders. We applied very effective numerical techniques to obtain the solutions of the model and simulations. Also, we present conditions of existence for a solution to the proposed epidemic model and to calculate the reproduction number in certain state conditions of the analyzed dynamic system. COVID-19 fractional order model for the case of Wuhan, China, is offered for analysis with simulations in order to determine the possible efficacy of Coronavirus disease transmission in the Community. For this reason, we employed the COVID-19 fractal fractional derivative model in the example of Wuhan, China, with the given beginning conditions. In conclusion, again the mathematical models with fractional operators can facilitate the improvement of decision-making for measures to be taken in the management of an epidemic situation. [ABSTRACT FROM AUTHOR]

The nonlinear Schrödinger equation (NLSE) is a fundamental equation in the field of nonlinear optics and plays an important role in the study of many physical phenomena. The present study introduces a new model that demonstrates the novelty of the paper and provides the advancement of knowledge in the area of nonlinear optics by solving a challenging problem known as the extended (3 + 1)-dimensional nonlinear conformable Kudryashov's equation (CKE) with generalized anti-cubic nonlinearity, which is a generalization of the NLSE to three spatial dimension and one temporal dimension for the first time. This work is significant because it advances our understanding of nonlinear optics and its applications to solve complex equations in physics and related disciplines. The extended hyperbolic function method (EHFM) and Nucci's reduction method are applied to the extended (3 + 1)-dimensional nonlinear CKE with generalized anti-cubic nonlinearity. The equation is solved by using the concept of conformable derivative, a recently developed operator in fractional calculus, which has advantages over other fractional derivatives in terms of accuracy and flexibility. The attained solutions include periodic singular, dark 1-soliton, singular 1-soliton, and bright 1-soliton which are visualized using 3D and contour plots. This study highlights the potential of using conformable derivative and the applied techniques to solve complex nonlinear differential equations in various fields. The obtained solutions and analysis will be useful in the design and analysis of optical communication systems and other related fields. Overall, this study contributes for the understanding of the dynamics of the extended (3+1)-dimensional nonlinear CKE and offers new insights into the use of mathematical techniques to tackle complex problems in physics and related fields. [ABSTRACT FROM AUTHOR]

This article extracts analytical solutions of the Fokas-Lenells equation describing pulse propagation in optical fibers and presents a comprehensive analysis of the analytical solutions. This paper focuses on deriving analytical, non-perturbative solutions for the Fokas-Lenells equation by reducing it to a system of ordinary differential equations using the Lie symmetry method. Three generators for the Lie algebra are obtained, and three reductions are explored by combining vector generators. These algebraic structures provide a powerful framework for simplifying complex mathematical and physical problems by revealing underlying symmetries and patterns. The graphical representations of obtained solutions are rendered. Besides, the influence of parameters within the equation on the behavior of the solutions has been demonstrated in the figures. These results contribute to a deeper understanding of the Fokas-Lenells equation and have implications in various fields of physics and engineering. [ABSTRACT FROM AUTHOR]