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The susceptible, exposed, infected, quarantined and vaccinated (SEIQV) population is accounted for in a mathematical model of COVID-19. This model covers the therapy for diseased people as well as therapeutic measures like immunization for susceptible people to enable understanding of the dynamics of the disease's propagation. Each of the equilibrium points, i.e., disease-free and endemic, has been proven to be globally asymptotically stable under the assumption that R0 is smaller or larger than unity, respectively. Although vaccination coverage is high, the basic reproduction number depends on the vaccine's effectiveness in preventing disease when R0 > 0. The Jacobian matrix and the Routh-Hurwitz theorem are used to derive the aforementioned analysis techniques. The results are further examined numerically by using the standard second-order Runge-Kutta (RK2) method. In order to visualize the global dynamics of the aforementioned model, the proposed model is expanded to examine some piecewise fractional order derivatives. We may comprehend the crossover behavior in the suggested model's illness dynamics by using the relevant derivative. To numerical present the results, we use RK2 method. [ABSTRACT FROM AUTHOR]

In this work, an epidemic model of a susceptible, exposed, infected and recovered SEIRtype is established for the distinctive dynamic compartments and epidemic characteristics of COVID-19 as it spreads across a population with a heterogeneous rate. The proposed model is investigated using a novel approach of fractional calculus known as piecewise derivatives. The existence theory is demonstrated through the establishment of sufficient conditions. In addition, result related to Hyers-Ulam stability is also derived for the considered model. A numerical method based on modified Euler procedure is also constructed to simulate the approximate solutions of the proposed model by employing various values of fractional orders. We testified the numerical results by using real available data of Japan. In addition, some results for the SEIR-type model are also presented graphically using the stochastic process, and the obtained results are discussed. [ABSTRACT FROM AUTHOR]

Recently, the area devoted to mathematical epidemiology has attracted much attention. Mathematical formulations have served as models for various infectious diseases. In this regard, mathematical models have also been used to study COVID-19, a threatening disease in present time. This research work is devoted to consider a SEIR (susceptible-exposed-infectious-removed) type mathematical model for investigating COVID-19 alongside a new scenario of fractional calculus. We consider piece-wise fractional order derivatives to investigate the proposed model for qualitative and computational analysis. The results related to the qualitative analysis are studied via using the tools of fixed point approach. In addition, the computational analysis is performed due to a significance of simulation to understand the transmission dynamics of COVID-19 infection in the community. In addition, a numerical scheme based on Newton's polynomials is established to simulate the approximate solutions of the proposed model by using various fractional orders. Additionally, some real data results are also shown in comparison to the numerical results. [ABSTRACT FROM AUTHOR]

The approximate controllability of a class of fractional stochastic evolution equations (FSEEs) are discussed in this study utilizes the Hilbert space by using Hilfer derivative. For different approaches, we remove the Lipschitz or compactness conditions and merely have to assume a weak growth requirement. The fixed point theorem, the diagonal argument, and approximation methods serve as the foundation for the study. The abstract theory is demonstrated using an example. A conclusion is given at the end. [ABSTRACT FROM AUTHOR]

Navier-Stokes (NS) equations dealing with gravitational force with time-fractional derivatives are discussed in this paper. These equations can be used to predict fluid velocity and pressure for a given geometry. This paper investigates the local and global existence and uniqueness of mild solutions to NS equations for the time fractional differential operator. We also work on the regularity effects of such types of equations were caused by orthogonal flow. [ABSTRACT FROM AUTHOR]

In this article, we discuss the existence and uniqueness results for mix derivative involving fractional operators of order β∈(1,2) and γ∈(0,1). We prove some important results by using integro-differential equation of pantograph type. We establish the existence and uniqueness of the solutions using fixed point theorem. Furthermore, one application is likewise given to represent our fundamental results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence-uniqueness, and Ulam Hyers stability (UHS) of solutions to a fractional-order pantograph differential equation (FOPDE) with two Caputo operators. Banach's fixed point (BFP) and Leray-alternative Schauder's are used to prove the existenceuniqueness of solutions. In addition, we discuss and demonstrate various types of Ulam-stability for our problem. Finally, an example is provided for clarity. [ABSTRACT FROM AUTHOR]

By employing practical and effective matrix algebra, this article aims to investigate specific properties of truncated exponential-Sheffer polynomials. This method provides a valuable tool for researching multivariable special polynomial properties. The properties and association between the Pascal functional and Wronskian matrices are used to build the recursive equations and differential equation for these polynomials, as well as for several members of the truncated exponential-Sheffer family. The corresponding results for the truncated exponential-associated Sheffer and truncated exponential-Appell families is specified, as well as some examples are given. Finally a conclusion with a truncated exponential-Sheffer polynomial identity is provided. [ABSTRACT FROM AUTHOR]