Investigation of Novel Piecewise Fractional Mathematical Model for COVID-19

The outbreak of coronavirus (COVID-19) began in Wuhan, China, and spread all around the globe. For analysis of the said outbreak, mathematical formulations are important techniques that are used for the stability and predictions of infectious diseases. In the given article, a novel mathematical system of differential equations is considered under the piecewise fractional operator of Caputo and Atangana–Baleanu. The system is composed of six ordinary differential equations (ODEs) for different agents. The given model investigated the transferring chain by taking non-constant rates of transmission to satisfy the feasibility assumption of the biological environment. There are many mathematical models proposed by many scientists. The existence of a solution along with the uniqueness of a solution in the format of a piecewise Caputo operator is also developed. The numerical technique of the Newton interpolation method is developed for the piecewise subinterval approximate solution for each quantity in the sense of Caputo and Atangana-Baleanu-Caputo (ABC) fractional derivatives. The numerical simulation is drawn against the available data of Pakistan on three different time intervals, and fractional orders converge to the classical integer orders, which again converge to their equilibrium points. The piecewise fractional format in the form of a mathematical model is investigated for the novel COVID-19 model, showing the crossover dynamics. Stability and convergence are achieved on small fractional orders in less time as compared to classical orders

A Time-Fractional Schrödinger Equation with Singular Potentials on the Boundary

A Schrödinger equation with a time-fractional derivative, posed in (0,∞)×I, where I=]a,b], is investigated in this paper. The equation involves a singular Hardy potential of the form λ(x−a)2, where the parameter λ belongs to a certain range, and a nonlinearity of the form μ(x−a)−ρ|u|p, where ρ≥0. Using some a priori estimates, necessary conditions for the existence of weak solutions are obtained

Computational analysis of rabies and its solution by applying fractional operator

Numerous novel concepts in fractional mathematics have been created to provide numerical models for a variety of real-world, engineering, and scientific challenges because of the kernel's memory and non-local effects. In this post, we have looked at a deadly illness known as rabies. For our analysis, we employed the Atangana–Baleanu fractional derivative in Caputo sense. Additionally, the mathematical answer was obtained by applying the Laplace transform. Our approach is distinct, and we illustrated the vital role immunizations play in limiting the spread of the illness using graphical data. Furthermore, in this article, we have shown that fractional order systems are preferable to integer order systems

Analytical Solution of the Local Fractional KdV Equation

This research work is dedicated to solving the n-generalized Korteweg–de Vries (KdV) equation in a fractional sense. The method is a combination of the Sumudu transform and the Adomian decomposition method. This method has significant advantages for solving differential equations that are both linear and nonlinear. It is easy to find the solutions to fractional-order PDEs with less computing labor

Nonlinear complex dynamical analysis and solitary waves for the (3+1)-D nonlinear extended Quantum Zakharov–Kuznetsov equation

This manuscript is a captivating exploration of the (3+1)-D nonlinear extended Quantum Zakharov–Kuznetsov (NLEQZK) equation, revealing its complex dynamics and solitary wave solutions. We unveil the general method behind this equation and transform it into an ordinary differential equation (ODE), then venture further by using the Galilean transformation to create a system of ODEs. Further, we journey through bifurcations, chaos, and other fascinating dynamical properties, culminating in the visualization and analysis of solitary wave solutions. From the elegant W-shaped solitons to singular solitons with unconventional characteristics and hybrid singular and periodic solitons, each is discussed in vivid detail. This work presents a significant advancement in understanding the unpredictable and intricate behavior of the model, inviting readers to explore the captivating world of non-linear waves and dynamical systems