The Existence Of Solution For Boundary Value Problem Of Three Classes Of Fractional Differential

Fractional order differential equation is a relatively new study area stems from the fractal phenomena, physics, engineering and other applied disciplines. As a promotion of classical differential equation with integer order, which can be used to explain and describe some real phenomenon better,and plays an increasingly important role in physics, engineering, finance, hyderlogy and other fields.Impulsive differential equation can be used to describe the evolution processes,which explain a change of state at certain moments of time, it is widely used in the real word.Therefore, we believe that it is meaningful to study the solution of fractional impulsive differential equation.I t can help us understand the real world better,an will be useful in human activities.In this paper, we apply the contraction mapping principle, Leray-Schauder fixed point theory, Krasnoselskii fixed point theory, and fractional order differential theory, to study the boundary value problem of several classes of fractional differential equations, we obtain the existence of solutions for these boundary value problems and apply the main results to concrete examples.The thesis is divided into four chapters according to contents.In Chapter one, we introduce the background of our research and main topics that we will study in the following chapters.In Chapter two, by using the contraction mapping principle, Leray-Schauder fixed point theory, Krasnoselskii fixed point theory, we obtain the existence of solution for three points boundary value problem of fractional differential equation as following where 1<α≤2 is real number,0<η<1,, a+b≠ 1,m+n≠1, cDa is Caputo fractional order differential operation, and f:[0,1] ×R→ R is continuous.In Chapter three, by using the contraction mapping principle, Krasnoselskii fixed point theory, fractional order differential theory, we consider the existence of solution for integral boundary value problem of fractional differential equation, wherea,β are real numbers, and 1<α≤2,0<β≤1, α -β> 1, a≠ 2, b≠ T(2—β), cDa is Caputo fractional order differential operation,f :[0, 1]× R→ R is continuous.In Chapter four, by using the contraction mapping principle, Leray-Schauder fixed point theory, fractional order differential theory, we consider the existence of solution for boundary value problem of fractional impulsive differential equation where J= [0,1], cDa is Caputo fractional order differential operation,f:J×R→R is...