Abstract
Abstract In this paper, we study the existence of positive solutions for a nonlinear fractional boundary value problem on the half-line. Based on the monotone iterative technique, we obtain the existence of positive solutions of a fractional boundary value problem and establish iterative schemes for approximating the solutions. As application, an example is presented to illustrate the main results. MSC:34A08, 34A12, 34B40.
Highlights
1 Introduction The initial and boundary value problems for nonlinear fractional differential equations arise from the study of models of viscoelasticity, control, porous media, etc. [, ]
In the past few years, the existence and multiplicity of positive solutions for nonlinear fractional boundary value problems have been widely studied by many authors
Liang and Zhang [ ] investigated the existence of three positive solutions for the following m-point fractional boundary value problem on an infinite interval by means of the Leggett-Williams fixed point theorems on cones
Summary
The initial and boundary value problems for nonlinear fractional differential equations arise from the study of models of viscoelasticity, control, porous media, etc. [ , ]. In the past few years, the existence and multiplicity of positive solutions for nonlinear fractional boundary value problems have been widely studied by many authors (see [ – ] and the references therein). Most of these papers only considered the existence of positive solutions of various boundary value problems.
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