Existence Result for Riemann-Liouville Fractional Differential Equation with Boundary Condition

Abstract

Investigation of existence property of Riemann-Liouville Fractional Differential Equation with Boundary Condition is done in this paper
\[{-D}^p_{0+}x\left(t\right)=f\left(t,x\left(t\right)\right),\ \ 0<t<1\ \ \ \ \ \ \]
\[x\left(0\right)=x'\left(0\right)=x''\left(0\right)=\dots =x^{\left(n-2\right)}\left(0\right)=0,\ \ x\left(1\right)=\lambda \int^1_0{x\left(s\right)ds}\]
the technique we have employed is coupled lower and upper solutions with fixed point theory on cone, where $2\le n-1<p\le n$, $p\in R$, is the order of Riemann-Liouville Fractional derivative and $0<\lambda <p$.