Existence of Solutions of Boudary Value Problem for Nonlinear Fractional Functional Differential Equations
|Keywords||Fractional differential equation Boundary value problem Conical Positive solution Fixed point theorem Time Delay Ascoli-Arzela theorem|
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 .