Opuscula Math. 37, no. 2 (2017), 281-301

Opuscula Mathematica

Existence of three solutions for impulsive nonlinear fractional boundary value problems

Shapour Heidarkhani
Massimiliano Ferrara
Giuseppe Caristi
Amjad Salari

Abstract. In this work we present new criteria on the existence of three solutions for a class of impulsive nonlinear fractional boundary-value problems depending on two parameters. We use variational methods for smooth functionals defined on reflexive Banach spaces in order to achieve our results.

Keywords: fractional differential equation, impulsive condition, classical solution, variational methods, critical point theory.

Mathematics Subject Classification: 34A08, 34B37, 58E05, 58E30, 26A33.

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  • Shapour Heidarkhani
  • Razi University, Faculty of Sciences, Department of Mathematics, 67149 Kermanshah, Iran
  • Massimiliano Ferrara
  • University Mediterranea of Reggio Calabria, Department of Law and Economics, Via dei Bianchi, 2 - 89131 Reggio Calabria, Italy
  • Giuseppe Caristi
  • University of Messina, Department of Economics, Via dei Verdi, 75, Messina, Italy
  • Amjad Salari
  • Razi University, Faculty of Sciences, Department of Mathematics, 67149 Kermanshah, Iran
  • Communicated by Marek Galewski.
  • Received: 2016-03-16.
  • Revised: 2016-06-20.
  • Accepted: 2016-06-22.
  • Published online: 2017-01-03.
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Cite this article as:
Shapour Heidarkhani, Massimiliano Ferrara, Giuseppe Caristi, Amjad Salari, Existence of three solutions for impulsive nonlinear fractional boundary value problems, Opuscula Math. 37, no. 2 (2017), 281-301, http://dx.doi.org/10.7494/OpMath.2017.37.2.281

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