一类带有p-Laplacian算子与积分边值条件的Caputo分数阶q-差分方程解的存在性

Existence of solutions to a class of Caputo fractional q-difference equations with p-Laplacian operator and integral boundary value conditions

研究了一类带有p-Laplacian算子与积分边界条件的Caputo分数阶q-差分方程:CDβq(ϕp(CDαqu(t)))+f(t,u(t))=0,t∈[0,1];u(1)=λ∫10 u(s)dqs,Dqu(0)=0,CDαqu(1)=bCDαqu(ξ).首先利用Arzelà-Ascoli定理与Schauder不动点定理证明了此类Caputo分数阶q-差分方程解的存在性,然后利用一个实例验证了文中所得的主要结论.

A class of Caputo fractional q-difference equations with p-Laplacian operator and integral boundary conditions are studied CDβq(ϕp(CDαqu(t)))+f(t,u(t))=0,t∈[0,1];u(1)=λ∫10 u(s)dqs,Dqu(0)=0,CDαqu(1)=bCDαqu(ξ).First,the Arzelà-Ascoli theorem and the Schauder fixed point theorem are used to prove the relevant conclusions of the existence of such Caputo fractional q-difference equations,and then an example is used to verify the main conclusions obtained in the article.