Existence of Solutions of Boudary Value Problem for Nonlinear Fractional Functional Differential Equations 

Author  LiGuoXiang 
Tutor  LiChengFu 
School  Xiangtan University 
Course  Applied Mathematics 
Keywords  Fractional differential equation Boundary value problem Conical Positive solution Fixed point theorem Time Delay AscoliArzela theorem 
CLC  O175.8 
Type  Master's thesis 
Year  2009 
Downloads  53 
Quotes  0 
Firstly, consider the twopoint boundary value problem of nonlinear fractional differential where 1 <α ≤ 2 is a real number , Dα αorder Riemann  Liouville derivative , f : [ 0,1] × [ 0 , ∞) → [ O, ∞) for our first Green's function is obtained , the differential equations into equivalent integral equation , and then take advantage of the fixed point theorem given the conditions of one or three positive solutions for boundary value problem . Next, study the following nonlinear fractional differential threepoint boundary value problem : where Dα α order derivative of the Riemann  Liouville meet the following Caratheodory conditions . Let's get the corresponding Green's function , thus the differential equations into equivalent integral equation . Based on this , the use of fixed point theorem , to obtain the results of the existence of the boundary value problem has a positive solution and multiple positive solutions . Finally, we discuss the nonlinear timedelay fractional differential equation boundary value problem where 1 < αa ≤ 2 is a real number , cD0 α is an α  order Caputo differential operator , f : [0 , T ] × CΥ → R , φ ∈ CΥ (: = C [Τ, 0]) and A ∈ R. using fixed point theorem is given to understand the existence results .