Abstract
In this paper, we consider a class of fractional boundary value problems with the derivative term and nonlinear operator term. By establishing new mixed monotone fixed point theorems, we prove these problems to have a unique solution, and we construct the corresponding iterative sequences to approximate the unique solution.
Highlights
In this paper, we consider the existence and uniqueness of nontrivial solutions of the following fractional boundary value problem: ⎧⎪⎪⎪⎪⎪⎨uD(β00+)(D= α0u+u(t)) = f (t, (0) = · · · =u(t), Dν0+ u(n–2)(0) u(t)) = 0, + g (t, u(t ), (Ku)(t))
Lv [1] studied the existence of positive solutions of the following multi-point boundary value problem:
[3] is the Banach contraction mapping principle. He showed the uniqueness of the problem (1.5) in [4] by the classic fixed point theorem of mixed monotone operators
Summary
We consider the existence and uniqueness of nontrivial solutions of the following fractional boundary value problem:. Lv [1] studied the existence of positive solutions of the following multi-point boundary value problem:. Lv [2] studied the existence of solutions for nonlinear fractional m-point boundary value problems involving p-Laplacian operators by the fixed point index theorem. The main tool of [3] is the Banach contraction mapping principle He showed the uniqueness of the problem (1.5) in [4] by the classic fixed point theorem of mixed monotone operators. Theorem 3.1 Let P be a normal cone in E, and let M, N : Ph,e × Ph,e −→ E be two mixed monotone operators, and the following conditions are satisfied:.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
