Well-posedness analysis and pseudo-Galerkin approximations using Tau Legendre algorithm for fractional systems of delay differential models regarding Hilfer (α,β)-framework set.

Fractional calculus serves as a versatile and potent tool for the modeling and control of intricate systems. This discussion debates the system of DFDEs with two regimes; theoretically and numerically. For theoretical analysis, we have established the EUE by leveraging the definition of Hilfer (α,β)-framework.

Existence, uniqueness, and galerkin shifted Legendre's approximation of time delays integrodifferential models by adapting the Hilfer fractional attitude.

Guaranteeing the uniqueness of the solution will simplify the analysis and provide a clear approximation of the considered problem. This article presents theoretical proof of the presence of a unique solution and leverages approximation for the time delay functions in integrodifferential models in the sense of the Hilfer fractional approach. Once the wellposedness discussion is done, our focus lies on utilizing the Galerkin pseudo-codes based on the OSLPs to generate an approximation by applying GSLM as follows: utilizing the OSLPs to replace the required functions in main Hilfer model, applying the Galerkin pseudo-codes, and transforming Hilfer model into an algebraic system of equations.

The fractional-order discrete COVID-19 pandemic model: stability and chaos.

This paper presents and investigates a new fractional discrete COVID-19 model which involves three variables: the new daily cases, additional severe cases and deaths. Here, we analyze the stability of the equilibrium point at different values of the fractional order. Using maximum Lyapunov exponents, phase attractors, bifurcation diagrams, the 0-1 test and approximation entropy (ApEn), it is shown that the dynamic behaviors of the model change from stable to chaotic behavior by varying the fractional orders.

The effect of the Caputo fractional difference operator on a new discrete COVID-19 model.

This study aims to generalize the discrete integer-order SEIR model to obtain the novel discrete fractional-order SEIR model of COVID-19 and study its dynamic characteristics. Here, we determine the equilibrium points of the model and discuss the stability analysis of these points in detail. Then, the non-linear dynamic behaviors of the suggested discrete fractional model for commensurate and incommensurate fractional orders are investigated through several numerical techniques, including maximum Lyapunov exponents, phase attractors, bifurcation diagrams and algorithm.

The prevalence of orbital complications among children and adults with acute rhinosinusitis.

Objective: To investigate orbital complications in children and adult with sinusitis.

Method: Patients attending ENT clinic with sinusitis from January 2010 until January 2012 were included. Patients were classified into two groups according to their age.