Acta mathematica scientia,Series A ›› 2018, Vol. 38 ›› Issue (6): 1162-1172.

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Existence and Uniqueness of Solutions to a Class of Anti-Periodic Boundary Value Problem of Fractional Differential Equations with p-Laplacian Operator

Yongzhen Yun,Youhui Su*(),Weimin Hu   

  1. 1 School of Mathematics and Physics, Xuzhou Institute of Technology, Jiangsu Xuzhou 221000
    2 School of Mathematics and Statistic, Yili Normal University, Xinjiang Yining 835000
  • Received:2016-11-15 Online:2018-12-26 Published:2018-12-27
  • Contact: Youhui Su E-mail:suyh02@163.com
  • Supported by:
    the NSFC(11361047);the NSFC(11501560);the Natural Science Foundation of Jiangsu Province(BK20151160);the Six Talent Peaks Project of Jiangsu Province(2013-JY-003);the 333 High-Level Talents Training Program of Jiangsu Province(BRA2016275)

Abstract:

In this paper, we investigate the existence and uniqueness of solutions to a class of anti-periodic boundary value problem of nonlinear Caputo fractional differential equations with p-Laplacian operator. First, the Green function of the fractional boundary value problem is given. By using the properties of p-Laplacian operator and the Banach contraction mapping principle, some new results on the existence and uniqueness of solutions to the fractional boundary value problem are obtained. As an application, two examples are given to illustrate our main results. In particular, the boundary value conditions of fractional differential equation which is studied in this paper contains the Caputo fractional differentiation.

Key words: Caputo fractional differentiation, Anti-periodic boundary value problem, Existence and uniqueness of solutions, p-Laplacian operator, Banach contraction mapping principle

CLC Number: 

  • O175.8
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