Abstract

In this paper, we consider a class of singular fractional differential equations with infinite-point boundary conditions. The fractional orders are involved in the nonlinearity of the boundary value problem, and the nonlinearity is allowed to be singular with respect to not only the time variable but also to the space variable. Firstly, we give Green’s function and establish its properties. Then, we utilize the sequential technique and regularization to investigate the existence of positive solutions. Finally, we give an example of application of our result.

Highlights

  • In this paper, we consider the following class of nonlinear singular fractional differential equations:⎧ ⎪⎨ Dα +u(t) + f (t, u(t), Dμ + u(t), Dμ + u(t), . . . , Dμ +n– u(t)) =, < t

  • Motivated by the results mentioned, in this paper, we utilize the sequential technique and regularization to investigate the existence of positive solutions of BVP ( . ), where u ∈ Cn– [, ]∩Cn– (, ) is said to be a positive solution of BVP ( . ) if and only if u satisfies ( . ) and u(t) > for any t ∈

  • By using the sequential technique and regularization on a cone, some new existence results are obtained for the case where the nonlinearity is allowed to be singular with respect to both time and space variables

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Summary

Introduction

We consider the following class of nonlinear singular fractional differential equations:. Many authors investigated the existence of positive solutions for fractional equation boundary value problems (see [ – ] and the references therein), and a great deal. Motivated by the results mentioned, in this paper, we utilize the sequential technique and regularization to investigate the existence of positive solutions of BVP By using the sequential technique and regularization on a cone, some new existence results are obtained for the case where the nonlinearity is allowed to be singular with respect to both time and space variables. In order to overcome the singularity, we utilize the sequential technique and regularization to testify the existence of positive solutions for problem

Preliminaries and lemmas
Findings
Conclusions

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