一类带p-Laplacian算子的分数阶微分方程边值问题解的存在性

The existence of solution for boundary value problem with p-Laplacian operator of fractional differential equations

该文运用Leray-Schauder非线性择抉和Krasnosel skiis不动点定理,讨论了一类在一致分数阶导数定义下含p-Laplacian算子的分数阶微分方程边值问题∅p(Tαx(t))′=f(t,x(t)),0≤t≤1,x(0)=Tαx(0)=0,x(1)=μ∫η0x(t)d t解的存在性.其中,1<α≤2,μ≥0,0<η≤1,∅p(s)=|s|p-2 s,(∅p)-1=∅q,p>1,p^(-1)+q^(-1)=1,Tα是一致分数阶导数,f:[0,1]×ℝ→ℝ是给定的连续函数.

In this paper,the existence of the solution with the p-Laplacian operator boundary value problem under the definition of conformable fractional derivative of the following form∅p(Tαx(t))′=f(t,x(t)),0≤t≤1,x(0)=Tαx(0)=0,x(1)=μ∫η0x(t)d t is discussed by using Leray-Schauder's nonlinear alternative and Krasnosel skiis fixed point theorem,where 1<α≤2,μ≥0,0<η≤1,∅p(s)=|s|p-2 s,(∅p)-1=∅q,p>1,p-1+q-1=1,Tαis the conformable fractional derivative,f:[0,1]×ℝ→ℝbe given a continuous function.