Abstract
In this work, we investigate the existence and uniqueness of the solutions for a class of nonlinear fractional differential equations with nonlocal integral boundary conditions. Our analysis relies on the fixed point index theory and a $u_{0}$ -positive operator. Examples are discussed for the illustration of the main work.
Highlights
1 Introduction We consider a class of nonlinear fractional differential equations with nonlocal integral boundary value conditions of this form:
Liu et al [ ] studied the existence of positive solutions and constructed two successively iterative sequences to approximate the solutions for the following fractional boundary value problem:
For n =, β =, the boundary conditions of ( . ) reduce to u( ) = u ( ) = u ( ) =, u( ) = λ η ds, which had been considered in Motivated by the work mentioned above, in this article we study the differential equations ( . ) by using u -positive operator and fixed point index theory under some conditions concerning the first eigenvalue with respect to the relevant linear operator
Summary
Wang and Zhang [ ] studied the existence and multiplicity of positive solutions for the following nonlinear fractional differential equations: Dα + u(t) + h(t)f (t, u(t)) = , < t < , n – < α ≤ n, u( ) = u ( ) = · · · = u(n– )( ) = , u( ) = Zhang [ ] studied the existence of positive solutions of the following nonlinear fractional differential equation with infinite-point boundary value conditions:
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