Positive solutions for fractional differential equation with a p-Laplacian operator

Abstract

This paper studies the following Caputo fractional differential equation with p-Laplacian of higher-order multi-point: Dβ0+(p(Dα0+u(t)))+f(t,u(t))=0,0≤t≤1,l-1<β≤l,n-1<α≤n,(p(Dα0+u(0)))(i)=0,i=0,1,2,…,l-1,u(i)(0)=0,i=1,2,…,n-1,u(1)=∑ m-2 i=1 aiu(ξi)。 Using the Schauder fixed point theorem, the existence of positive solution is obtained for the above boundary value problems. An example is presented to illustrate our main theorem.

Keywords

• ordinary differential equation
• p-Laplacian
• fractional differential equation
• multi-point
• positive solution
• fixed point theorem