Journal of Applied Mathematics and Computing

, Volume 41, Issue 1, pp 119–131

Existence of solutions of two-point boundary value problems for fractional p-Laplace differential equations at resonance

Original Research

DOI: 10.1007/s12190-012-0598-0

Cite this article as:
Tang, X., Yan, C. & Liu, Q. J. Appl. Math. Comput. (2013) 41: 119. doi:10.1007/s12190-012-0598-0

Abstract

In this paper, we consider the following two-point boundary value problem for fractional p-Laplace differential equation
https://static-content.springer.com/image/art%3A10.1007%2Fs12190-012-0598-0/MediaObjects/12190_2012_598_Equa_HTML.gif
where \(D^{\alpha}_{0^{+}}\), \(D^{\beta}_{0^{+}}\) denote the Caputo fractional derivatives, 0<α,β≤1, 1<α+β≤2. By using the coincidence degree theory, a new result on the existence of solutions for above fractional boundary value problem is obtained. These results extend the corresponding ones of ordinary differential equations of integer order. Finally, an example is inserted to illustrate the validity and practicability of our main results.

Keywords

Caputo fractional derivativep-Laplace differential equationTwo-point boundary value problemResonanceCoincidence degree theory

Mathematics Subject Classification

34A0834B15

Copyright information

© Korean Society for Computational and Applied Mathematics 2012

Authors and Affiliations

  1. 1.College of Mathematics and PhysicsJinggangshan UniversityJi’anP.R. China
  2. 2.College of Electronics and Information EngineeringJinggangshan UniversityJi’anP.R. China