Abstract
This paper is to investigate the existence and uniqueness of solutions for an integral boundary value problem of new fractional differential equations with a sign-changed parameter in Banach spaces. The main used approach is a recent fixed point theorem of increasing Ψ − h , r -concave operators defined on ordered sets. In addition, we can present a monotone iterative scheme to approximate the unique solution. In the end, two simple examples are given to illustrate our main results.
Highlights
We show that T: Ph,r ⟶ E satisfied the definition of Ψ − (h, r)-concave operator
We show that T: P ⟶ P satisfied the definition of Ψ − (h, θ)-concave operator
We study an integral boundary value problem (4) with sign-changed parameter in Banach spaces
Summary
With the intensive development of theory and applications of fractional calculus, fractional differential equations have been paid great interest in many fields and different boundary conditions of fractional differential equations have attracted much attention, see [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42]. U(1) ρ u(t)dt, where 2 < β ≤ 3, 0 < ρ < β, J [0, 1], Dβ0+ is the R-L fractional derivative, f: J × K ⟶ K is continuous, here K is a normal cone in E, and θ denotes the zero element of E. ey Complexity obtained the existence results of positive solutions by using fixed point index theory of condensing mapping. Motivated by these works, we consider the following new form of fractional differential equation with an integral boundary condition:. We do not need the existence of upper-lower solutions, which is a critical condition in many articles
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