American scientific publishing group

This paper investigates a fractional-order SEIR model to study the dynamics of infectious diseases, specifically COVID-19, by incorporating memory effects through fractional derivatives. The model’s formulation enhances the understanding of epidemic dynamics by considering disease transmission, recovery, and mortality rates under fractional calculus. Stability analyses are conducted for the disease-free equilibrium (DFE) and the pandemic fixed point (PFP), identifying critical conditions for finite-time stability using Lyapunov functions and fractional derivatives. Numerical simulations validate theoretical findings, demonstrating finitetime stabilization around the equilibrium points under realistic parameter settings. The results underscore the advantages of fractional-order modeling in capturing complex epidemic dynamics and highlight its potential to inform public health intervention strategies.

In this paper, we introduce a new subclass of analytic functions denoted byMp,qΣ (∝, β), where we use the subordination relationship between the Mittag-Leffler function and the (p, q)-derivative of F(z) to define this new class. By employing the Taylor-Maclaurin series expansion, we focus on estimating the bounds for the coefficients |a2| and |a3|. Moreover, we establish Fekete Szeg¨o inequalities for functions within this class.

This work is dedicated to advancing the approximation of initial value problems through the introduction of an innovative and superior method inspired by the Euler-Maclaurin formula. This results in a higher-order implicit corrected method that outperforms the Runge-Kutta method in terms of accuracy. We derive an error bound for the Euler-Maclaurin higher-order method, showcasing its stability, convergence, and greater efficiency compared to the conventional Runge-Kutta method. To substantiate our claims, numerical experiments are provided, highlighting the exceptional efficiency of our proposed method over the traditional well-known methods. In conclusion, the proposed method consistently outperforms the Runge-Kutta method experimentally in all practical problems.

In this paper, we stady a mathematical model based on a system of fractional-order differential equations to describe the dynamics of the Lengyel–Epstein chemical reaction, which is well known for exhibiting oscillatory behavior. The use of fractional derivatives allows in chemical processes compared to classical integer-order models. We specifically focus on analyzing the stability of the system’s positive equilibrium point by applying fractional calculus techniques. The stability conditions are derived and discussed in the context of the fractional-order parameters. To validate the theoretical findings, we perform numerical simulations using the Forward Euler method adapted for fractional-order systems. These simulations illustrate the impact of the fractional order on the system’s dynamic behavior and confirm the analytical results regarding equilibrium stability.

This work is dedicated to advancing the approximation of initial value problems through the introduction of an innovative and superior method inspired by the Euler-Maclaurin formula. This results in a higher-order implicit corrected method that outperforms Taylor’s and Runge–Katta’s methods in terms of accuracy. We derive an error bound for the Euler-Maclaurin higher-order method, showcasing its stability, convergence, and greater efficiency compared to the conventional Taylor and Runge-Katta methods. To substantiate our claims, numerical experiments are provided, highlighting the exceptional efficiency of our proposed method over the traditional well-known methods.