Well-posedness analysis and pseudo-Galerkin approximations using Tau Legendre algorithm for fractional systems of delay differential models regarding Hilfer (α,ß)-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,ß)-framework. Our investigation involved the examination of the possessions of the FRD, FCD, and FHD, utilizing their forcefulness and qualifications to convert the concerning delay system into an equivalent one of fractional DVIEs. By employing the CMT, we have successfully demonstrated the prescribed requirements. For numerical analysis, the Galerkin algorithm was implemented by leveraging OSLPs as a base function. This algorithm allows us to estimate the solution to the concerning system by transforming it into a series of algebraic equations. By employing the software MATHEMATICA 11, we have effortlessly demonstrated the requirements estimation of the nodal values. One of the key advantages of the deployed algorithm is its ability to achieve accurate results with fewer iterations compared to alternative methods. To validate the effectiveness and precision of our analysis, we conducted a comprehensive evaluation through various linear and nonlinear numerical applications. The results of these tests, accompanied by figures and tables, further support the superiority of our algorithm. Finally, an analysis of the numerical algorithm employed was provided along with insightful suggestions for potential future research directions.

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. Herein, the wellposedness is proven by utilizing the fixed point of Banach and the principle of contraction mapping. The proposed scheme is shown to provide efficient, flawless, and expedient solutions for the needed Hilfer fractional delay model. Whilst, the effectiveness of the approach is demonstrated by various delayed examples in comparison with the classical solution. Tabulated and plotted results of the study provide a novel reliable scheme for handling such a Hilfer delayed integrodifferential model. Eventually, valuable noteworthy points and suggestions for future endeavors have been offered.

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. Besides showing that the fractional discrete model fits the real data of the pandemic, the simulation findings also show that the numbers of new daily cases, additional severe cases and deaths exhibit chaotic behavior without any effective attempts to curb the epidemic.

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 C 0 algorithm. Finally, we fitted the model with actual data to verify the accuracy of our mathematical study of the stability of the fractional discrete COVID-19 model.

A prevalencia de complicacoes orbitarias entre criancas e adultos com rinossinusite aguda / The prevalence of orbital complications among children and adults with acute rhinosinusitis

OBJETIVO: Investigar as complicações orbitais em crianças e adultos com sinusite. MÉTODO: Os pacientes que frequentam clínica de Otorrinolaringologia com sinusite de janeiro de 2010 até janeiro de 2012 foram incluídos. Os pacientes foram classificados em dois grupos, de acordo com sua idade. O primeiro incluiu crianças idade inferior a 16 anos e, o segundo, pacientes com mais de 16 anos. Quadro clínico, seio envolvido, gestão e resultados foram comparados. RESULTADOS: O número total de pacientes foi 616. Complicações orbitais foram observadas em 36 pacientes (5,8%). Destes, 26 pacientes (72,2%) eram crianças (21 tinham presseptal e cinco tiveram celulite orbitária) e dez pacientes (27,8%) eram adultos (cinco com pré-septal, três com celulite orbitária e dois com abscesso). A complicação mais comum foi celulite orbital presseptal (72,2%), seguida de celulite e abcesso orbital (22,2% e 5,6%, respectivamente). O seio mais comum envolvido foi etmoidal em crianças e sinusopatia mista em adultos. A maioria dos pacientes respondeu ao tratamento médico. CONCLUSÃO: As complicações orbitárias da sinusite são mais comuns em crianças do que em adultos e têm prognóstico favorável. .

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. First involved children aged less than 16 and second included adults older than 16 years. Clinical picture, sinus involved, management and outcome were compared. RESULTS: The total number of patients were 616. Orbital complications were seen in 36 patients (5.8%). Twenty six patients (72.2%) were children (21 had preseptal and 5 had orbital cellulitis) and ten patients (27.8%) were adults (5 with preseptal, three with orbital cellulitis and 2 with abscess). The most common orbital complication was preseptal cellulitis (72.2%) followed by orbital cellulitis and abscess (22.2% and 5.6% respectively). The commonest sinus involved was ethmoidal in children and mixed sinus pathology in adults. The majority of patients responded to medical treatment. CONCLUSION: Orbital complications of sinusitis are commoner in children than adults and have favorable prognosis. Keywords: Sinusitis, cellulitis, preseptal, abscess. .

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. First involved children aged less than 16 and second included adults older than 16 years. Clinical picture, sinus involved, management and outcome were compared. RESULTS: The total number of patients were 616. Orbital complications were seen in 36 patients (5.8%). Twenty six patients (72.2%) were children (21 had preseptal and 5 had orbital cellulitis) and ten patients (27.8%) were adults (5 with preseptal, three with orbital cellulitis and 2 with abscess). The most common orbital complication was preseptal cellulitis (72.2%) followed by orbital cellulitis and abscess (22.2% and 5.6% respectively). The commonest sinus involved was ethmoidal in children and mixed sinus pathology in adults. The majority of patients responded to medical treatment. CONCLUSION: Orbital complications of sinusitis are commoner in children than adults and have favorable prognosis. KEYWORDS: Sinusitis, cellulitis, preseptal, abscess.