UPPER AND LOWER SOLUTIONS METHOD FOR
FRACTIONAL DIFFERENTIAL EQUATIONS
WITH INTEGRAL BOUNDARY CONDITIONS

Abstract

In this paper, we investigate the existence and uniqueness of positive solutions of boundary value problems (BVPs) for fractional differential equations (FDEs) with boundary conditions (BCs) involving the Riemann-Liouville (RL) fractional derivative of the form: \begin{equation*}
\left\{
\begin{array}{c}
-D_{0+}^{\sigma }x(t)=f(t,x(t)),\ ...
...0}^{1}x(s)ds,\quad 0<\vartheta <\sigma ,
\end{array}%
\right.
\end{equation*} where $2\leq n-1< \sigma \leq n$ and $\sigma\in \mathbb{R}$. The technique employed is coupled lower and upper solutions with fixed point theory on cone. An example is presented to justify our results.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 33
Issue: 3
Year: 2020

DOI: 10.12732/ijam.v33i3.8

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