Solutions Of Some Boundary Value Problems For Fractional Impulsive Differential Equations With P-Laplacian Operators

In recent decades,the model of differential equations has been widely applied in all directions.It has been found that non-linear fractional differential equations can describe natural phenomena better than integer-order differential equations.Therefore the theory of fractional differential equations has been used in meteorology,chemistry,electromagnetism,mechanics and materials.This paper mainly uses Banach contractive mapping principle,Leray-Schauder fixed point theorem,Krsnoasel’ skii fixed point theorem and so on.class Solutions of Boundary Value Problems for Fractional Impulsive Differential Equations with p-Laplacian Operators.In the first part of the introduction,the research background and research status of fractional impulsive differential equations are introduced.In Chapter 2.We consider the fractional impulsive differential equationsIn here,CD01+α is the standard Caputo fractional derivative,α-1<β≤1,a≥0,b>0,c≥0,d>O,(δ=bc+a(c+d/Γ(2-β))),x0,x1∈R,f∈C(J×R,R),Ik,Qk,J=[0,1].In chapter 3,we consider the boundary value problem of fractional impulsive differential equationsIn here,CD0+α,CD0+β is the standard Caputo fractional derivative,a≥0,b>0,c≥0,d>0,δ=a(c-d)+bc>0,0<α,β<1,1<α+β<2;f∈C(JxR,R),Ik,Qk∈R,J=[0,1].In chapter 4,we consider the existence and uniqueness of the solution of the integral boundary value problem for fractional impulsive differential equations In here,CD0+α,CD0+β is the standars Caputo differential dericvative,1<α≤2,0<β≤1,f∈C(J×X,X),Ik,Qk∈C(X,X),J=[0,1],J’=J\{t1,t2,...,tm},0=t0<t1<...<tm=1,q1,q2:X→X.In chapter 5,we consider the existence and uniqueness of a class of fractional differential equations with special forms of anti-periodic boundary conditions for a class of nonlinear terms with Caputo fractional differentialsIn here,CD0+α,CD0+β is the standard Caputo fractional derivative,1<α≤2,0<β≤1,β+1<α,α’,β’>1,λ,η∈R,0=t0<t1<...<tm+1=1,J’=J\{t1,t2,...,tm},f∈C(J× X,X),Ik,Qk∈C(R,R),q1,q2 ∈ C[0,1].