φ-Hilfer分数阶共振边值问题解的存在性  

Existence of Solutions ofφ-Hilfer Fractional Order Boundary Value Problems at Resonance

作　　者：司换敏 江卫华[1] SI Huanmin;JIANG Weihua(School of Sciences,Hebei University of Science and Technology,Shijiazhuang 050018,China)

机构地区：[1]河北科技大学理学院,石家庄050018

出　　处：《吉林大学学报（理学版）》2023年第5期1019-1028,共10页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11775169);河北省自然科学基金(批准号:A2018208171).

摘　　要：用Mawhin的重合度理论研究共振情形下φ-Hilfer分数阶Riemman-Stieltjes积分边值问题■解的存在性,其中n-1<α≤n,0≤β≤1,γ=α+nβ-αβ,n=1,2,…,φ∈C^(n)[0,1]且φ′(t)>0于[0,1],A(t)是一个有界变差函数.结果表明,在合适的Banach空间中,φ-Hilfer分数阶微分方程在Riemman-Stieltjes积分边界条件下的解存在.By using Mawhin’s coincidence degree theory,we study the existence of solutions for theφ-Hilfer fractional order Riemman-Stieltjes integral boundary value problem ■ in resonance case,where n-1<α≤n,0≤β≤1,γ=α+nβ-αβ,n=1,2,…,φ∈C^(n)[0,1]and for all t∈[0,1]we haveφ′(t)>0,A(t)is a bounded variation function.The results show that the solutions ofφ-Hilfer fractional differential equation exist under the Riemann-Stieltjes integral boundary value conditions in suitable Banach spaces.

关 键 词：φ-Hilfer分数阶导数 Mawhin的重合度理论 FREDHOLM算子 边值问题 共振 

分 类 号：O175.8[理学—数学]