Fractional Delay Differential Equations And Its Applications In HIV Infection Of CD4~+T-cell

In recent years, with the boom of fractional calculus study, it is rapid growth for theresearch of fractional delay diferential equations and it’s applications. First, we study theexistence and uniqueness of solutions of fractional model with nonlocal boundary value, butalso simulate the numerical solution of equations. Secondly, we introduce fractional systemsinto the dynamic model of HIV infection, because of fractional diferential equations withmemory function, the important feature of the immune response is memory function exactly.Furthermore, delay is present in a biological system all the time. We introduce fractionaldelay diferential equations and its applications in HIV infection of CD4+T-cell. There aresome new results.This article consists of the following components:The first chapter introduces the research background of fractional delay diferential e-quations and its applications in HIV infection of CD4+T-cell.The second chapter introduces relevant prior knowledge.The third chapter studies the problems about fractional diferential equations with nonlo-cal initial boundary conditions. By using fixed point theorem, we further study the existenceand uniqueness of the equations under some certain assumptions.The fourth chapter discusses the fractional diferential equations with two fractionalderivative boundary value problem, we study the existence and uniqueness of equations. Inaddition, we use G2algorithm and simulate fractional Langevin equation with and withoutwhite noise.The fifth chapter considers the fractional HIV infection model, and we consider the mod-el to increase logistic growth item、delay term and treatment rates item. We apply the moreaccurate and more appropriate method to research stability of the system. At last, with thepredictor-corrector method, we describe trajectory system, and confirm the theoretical stabil-ity.Chapter6discusses fractional delay model about HIV infection CD4+T cells, we consid-er the problem of proliferation about CD4+T-cell under antiretroviral therapy. Furthermore,we calculate the basic reproduction number R0, Uninfected equilibrium point E0, two infectedequilibrium points E**and E, and determine the stability of the equilibrium point. Chapter7of this paper, we summarize the main and determine the direction of futureresearch.