Abstract
This paper concerns the boundary value problem of a class of fractional differential equations involving the Riemann-Liouville fractional derivative with nonlocal integral boundary conditions. By using the properties of the Green’s function and the monotone iteration technique, one shows the existence of positive solutions and constructs two successively iterative sequences to approximate the solutions, especially numerically simulates the conclusion by an example.
Highlights
We investigate a class of nonlinear fractional differential equations with nonlocal integral boundary value conditions of the form
Motivated by the works mentioned above, in this article we study the differential equations ( . ) by using the fixed point theorem for increasing operators on the order intervals
Author details 1School of Mathematics, Jilin University, Changchun, 130012, P.R. China
Summary
We investigate a class of nonlinear fractional differential equations with nonlocal integral boundary value conditions of the form. Ahmad and Nieto [ ] studied the existence and the uniqueness of solutions to the following nonlinear fractional integro-differential equation: Dα +u(t) = f (t, u(t), (φu)(t), (ψu)(t)), t ∈ [ , T], Dα +– u( +) = , Dα +– u( +) = νI α+– u(η), Liu et al Advances in Difference Equations (2015) 2015:187 where < α ≤ , < η < T, ν is a constant, f : [ , T] × R × R × R → R is continuous, and t (φx)(t) = γ (t, s)x(s) ds, t (ψx)(t) = δ(t, s)x(s) ds with γ and δ being continuous functions on [ , T] × [ , T]. Zhang et al [ ] studied the existence of positive solutions to the following fractional boundary value problem:. In Section , an example is given to numerically simulate our conclusion
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