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

Original Research


In this paper, we consider the following two-point boundary value problem for fractional p-Laplace differential equation 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.


Caputo fractional derivative p-Laplace differential equation Two-point boundary value problem Resonance Coincidence degree theory 

Mathematics Subject Classification

34A08 34B15 

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

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