具有适型分数阶导数的边值问题的正解

数学物理学报 ›› 2017, Vol. 37 ›› Issue (1): 82-91.

具有适型分数阶导数的边值问题的正解

董晓玉, 白占兵, 孙苏菁

山东科技大学数学与系统科学学院山东青岛 266590

收稿日期:2016-05-13 修回日期:2016-11-07 出版日期:2017-02-26 发布日期:2017-02-26
作者简介:白占兵,E-mail:zhanbingbai@163.com
基金资助:
国家自然科学基金（11571207）、泰山学者项目和山东科技大学研究生科技创新项目（SDKDYC 170343）

Positive Solutions for Some Boundary Value Problems with Conformable Fractional Differential Derivatives

Dong Xiaoyu, Bai Zhanbing, Sun Sujing

Department of Mathematics, College of Mathematics and System Science, Shandong University of Science and Technology, Shondong Qingdao 266590

Received:2016-05-13 Revised:2016-11-07 Online:2017-02-26 Published:2017-02-26
Supported by:
Supported by the NSFC (11571207), the Taishan Scholar Project and SDUST Graduate Innovation Project (SDKDYC 170343)

摘要/Abstract

摘要：

该文研究一类非线性分数阶微分方程边值问题D^αu（t）+f（t，u（t））=0，0 < t < 1，u（0）=u（1）=0的可解性，其中1 < α ≤ 2是实数，D^α是适型分数阶导数，f：[0，1]×[0，∞）→[0，∞）是连续函数.研究的难点之一是相应的Green函数G（t，s）在s=0处是奇异的.利用逼近法和锥上的不动点定理，得到了正解的存在性和多解性.

关键词: 适型分数阶导数, 奇异Green函数, 锥上不动点定理

Abstract:

In this paper, we establish the solvability of a class nonlinear fractional differential equation boundary value problem D^αu(t)+f(t, u(t))=0, 0 < t < 1, u(0)=u(1)=0, where 1 < α ≤ 2 is a real number, D^α is the conformable fractional derivative, and f:[0, 1]×[0, ∞)→[0, ∞) is a continuous function. One of the difficulty here is the corresponding Green's function G(t, s) is singular at s=0. By the use of approach method and fixed-point theorems on cone, some existence and multiplicity results of positive solutions are acquired.

Key words: Conformable fractional derivative, Singular Green's function, Fixed-point theorems on cone

中图分类号:

O175.08

董晓玉, 白占兵, 孙苏菁. 具有适型分数阶导数的边值问题的正解[J]. 数学物理学报, 2017, 37(1): 82-91.

Dong Xiaoyu, Bai Zhanbing, Sun Sujing. Positive Solutions for Some Boundary Value Problems with Conformable Fractional Differential Derivatives[J]. Acta mathematica scientia,Series A, 2017, 37(1): 82-91.

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