Abstract
In this paper, a fractional multi-point boundary value problem is considered. By using the fixed point index theory and Krein-Rutman theorem, some results on existence are obtained.
Highlights
Fractional differential equations have been of great interest recently
This is due to the intensive development of the theory of fractional calculus itself as well as its applications
Apart from diverse areas of mathematics, fractional differential equations arise in rheology, dynamical processes in self similar and porous structures, electrical networks, visco-elasticity, chemical physics, and many other branches of science
Summary
Fractional differential equations have been of great interest recently. This is due to the intensive development of the theory of fractional calculus itself as well as its applications. There are some papers dealing with the existence and multiplicity of solution to the nonlinear fractional differential equations boundary value problems, see [8]-[14]. Zhao [11] investigated the existence and uniqueness of positive solutions for a local boundary value problem of fractional differential equation. (2014) Positive Solutions for Fractional Differential Equations with Multi-Point Boundary Value Problems. (H2) f : [0,1]× R+ → R+ satisfied Carathéodory condition,that is f (⋅,u) is measurable for each fixed u ∈ R+ and f (t,⋅) is continuous for a.e. t ∈[0,1]. (H3) ∀l > 0, ∃L > 0, f (t,u) < L where u ∈[0,l] ; a.e. t ∈[0,1]
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