Dissertation > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations > Boundary Value Problems

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 Ascoli-Arzela theorem
CLC O175.8
Type Master's thesis
Year 2009
Downloads 53
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Firstly, consider the two-point boundary value problem of nonlinear fractional differential where 1 <α ≤ 2 is a real number , Dα α-order 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 three-point 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 time-delay 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 .

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