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.
This paper presents a restricted SIR mathematical model to analyze the evolution of a contagious infectious disease outbreak (COVID-19) using available data. The new model focuses on two main concepts: first, it can present multiple waves of the disease, and second, it analyzes how far an infection can be eradicated with the help of vaccination. The stability analysis of the equilibrium points for the suggested model is initially investigated by identifying the matching equilibrium points and examining their stability. The basic reproduction number is calculated, and the positivity of the solutions is established. Numerical simulations are performed to determine if it is multipeak and evaluate vaccination's effects. In addition, the proposed model is compared to the literature already published and the effectiveness of vaccination has been recorded.
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.
The research described in this paper follows the hypothesis that the monomiality principle leads to novel results that are consistent with past knowledge. Thus, in line with prior facts, our aim is to introduce the Δh multi-variate Hermite polynomials ΔhHm(q1,q2,⋯,qr;h). We obtain their recurrence relations by using difference operators. Furthermore, symmetric identities satisfied by these polynomials are established. The operational rules are helpful in demonstrating the novel characteristics of the polynomial families, and thus the operational principles satisfied by these polynomials are derived and will prove beneficial for future observations.
This study follows the line of research that by employing the monomiality principle, new outcomes are produced. Thus, in line with prior facts, our aim is to introduce the Δh multi-variate Hermite Appell polynomials ΔhHAm[r](q1,q2,⋯,qr;h). Further, we obtain their recurrence sort of relations by using difference operators. Furthermore, symmetric identities satisfied by these polynomials are established. The operational rules are helpful in demonstrating the novel characteristics of the polynomial families and thus operational principle satisfied by these polynomials is derived and will prove beneficial for future observations. Further, a few members of the Δh Appell polynomial family are considered and their corresponding results are derived accordingly.
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