Two generalized Lyapunov-type inequalities for a fractional p-Laplacian equation with fractional boundary conditions

Yang Liu; Dapeng Xie; Dandan Yang; Chuanzhi Bai

doi:10.1186/s13660-017-1374-3

Two generalized Lyapunov-type inequalities for a fractional p-Laplacian equation with fractional boundary conditions

J Inequal Appl. 2017;2017(1):98. doi: 10.1186/s13660-017-1374-3. Epub 2017 May 3.

Authors

Yang Liu¹, Dapeng Xie¹, Dandan Yang², Chuanzhi Bai²

Affiliations

¹ Department of Mathematics, Hefei Normal University, Hefei, Anhui 230061 P.R. China.
² Department of Mathematics, Huaiyin Normal University, Huaian, Jiangsu 223300 P.R. China.

Abstract

In this paper, we investigate the existence of positive solutions for the boundary value problem of nonlinear fractional differential equation with mixed fractional derivatives and p-Laplacian operator. Then we establish two smart generalizations of Lyapunov-type inequalities. Some applications are given to demonstrate the effectiveness of the new results.

Keywords: Guo-Krasnoselskii fixed point theorem; Lyapunov-type inequality; fractional boundary value problem; p-Laplacian operator.