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In the current article, we studied the novel corona virus (2019-nCoV or COVID-19) which is a threat to the whole world nowadays. We consider a fractional order epidemic model which describes the dynamics of COVID-19 under nonsingular kernel type of fractional derivative. An attempt is made to discuss the existence of the model using the fixed point theorem of Banach and Krasnoselskii's type. We will also discuss the Ulam-Hyers type of stability of the mentioned problem. For semi analytical solution of the problem the Laplace Adomian decomposition method (LADM) is suggested to obtain the required solution. The results are simulated via Matlab by graphs. Also we have compare the simulated results with some reported real data for Commutative class at classical order. [ABSTRACT FROM AUTHOR]

The study is devoted to demonstrating the hypothesis necessary for the existence, uniqueness and at least one solution of implicit Hadamard fractional differential equations with nonlocal semi-coupled fractional integro-multipoints boundary conditions. Using Banach contraction principle, the uniqueness result is obtained. Leray–Schauder fixed point theorem supports the results of at least one solution of the aforementioned system. Additionally, By two different approaches, Hyers–Ulam stabilities are discussed for the proposed system. For verification, an example is presented. Through Remarks, ordinary differential equation of second-order with periodic and initial conditions are given by fixing some parameters in the suggested system. [ABSTRACT FROM AUTHOR]

A fractional system for transmission dynamics behavior of influenza infection with two strains is investigated and applied to the qualitative assess of crossing immunities on the expansion of the disease. The generalized mathematical model is significantly more informative regarding the infection outbreak and gives a deep description of the infection's dynamic process. We firstly take the integer order system given in current literature and then we globalize it by applying the Caputo operator of fractional derivatives. Moreover, we present the rudimentary results of the Caputo operator for the examination of the system, comprising the basic reproduction number R 0 and equilibrium points stabilities with the help of the Routh–Hurwitz and the Lyapunov operators techniques. We also focus on the approximate root. For simulations, we apply the famous generalize predictor–corrector Adams–Bashforth Moulton method, which shows the impact of two strains of influenza disease. • Formulation of the fractional model. • Existence and uniqueness of the global positive solution are obtained. • Deterministic analysis of the model. • Stability and approximate of the results. • Numerical simulation of the model. [ABSTRACT FROM AUTHOR]

This paper provides the effects of nutrients concentrations on the algae growth via solitary wave analysis and classical existence theory. There is a well known Diffusive Nutrient-Algae model based on the Sanyang wetland, is under consideration. The new families of exact solutions which represent nutrient concentration and algae density in different form are observed using the ϕ 6 -model expansion. Furthermore, the existence of these solutions are also discussed under different restrictive conditions and variables of nutrient concentration and algae density are represented in hyperbolic, trigonometric and rational forms. The graphics of these solutions are also sketched in 3D and 2D representations. [ABSTRACT FROM AUTHOR]