No abstract

In this paper, we prove the existence and uniqueness of solutions for a system of fractional differential equations with Riemann-Liouville integral boundary conditions of different order. Our results are based on the nonlinear alternative of Leray-Schauder type and Banach's fixed-point theorem. An illustrative example is also presented.

The Dynkin algebras are the hereditary artin algebras of finite representation type. The paper determines the number of complete exceptional sequences for any Dynkin algebra. Since the complete exceptional sequences for a Dynkin algebra of Dynkin type ∆ correspond bijectively to the maximal chains in the lattice of non-crossing partitions of type ∆, the calculations presented here may also be considered as a categorification of the corresponding result for non-crossing partitions.

Two virus infection models with antibody immune response and chronically infected cells are proposed and analyzed. Bilinear incidence rate is considered in the first model, while the incidence rate is given by a saturated functional response in the second one. One main feature of these models is that it includes both short-lived infected cells and chronically infected cells. The chronically infected cells produce much smaller amounts of virus than the short-lived infected cells and die at a much slower rate. Our mathematical analysis establishes that the global dynamics of the two models are determined by two threshold parametersR0andR1. By constructing Lyapunov functions and using LaSalle's invariance principle, we have established the global asymptotic stability of all steady states of the models. We have proven that, the uninfected steady state is globally asymptotically stable (GAS) ifR0<1, the infected steady state without antibody immune response exists and it is GAS ifR1<1<R0, and the infected steady state with antibody immune response exists and it is GAS ifR1>1. We check our theorems with numerical simulation in the end.

This paper is devoted to examine the thermally stratified mixed convection flow of an Oldroyd-B fluid. The stagnation point flow towards a stretching surface is discussed. The boundary layer flow and energy equations are employed. Resulting partial differential systems are converted into the ordinary differential systems. Convergent series solutions for velocity and temperature are developed and analyzed. Numerical values of Nusselt number is computed and examined. Comparison of present study is shown with the previous results. It is found that velocity decreases through the stratified effects.