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The European Physical Journal Special Topics

, Volume 222, Issue 8, pp 1857–1874 | Cite as

Presentation of solutions of impulsive fractional Langevin equations and existence results

Impulsive fractional Langevin equations
  • J. WangEmail author
  • M. Fec̆kan
  • Y. Zhou
Regular Article

Abstract

In this paper, a class of impulsive fractional Langevin equations is firstly offered. Formula of solutions involving Mittag-Leffler functions and impulsive terms of such equations are successively derived by studying the corresponding linear Langevin equations with two different fractional derivatives. Meanwhile, existence results of solutions are established by utilizing boundedness, continuity, monotonicity and nonnegative of Mittag-Leffler functions and fixed point methods. Further, other existence results of nonlinear impulsive problems are also presented. Finally, an example is given to illustrate our theoretical results.

Keywords

European Physical Journal Special Topic Fractional Derivative Existence Result Fractional Calculus Contraction Mapping 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© EDP Sciences and Springer 2013

Authors and Affiliations

  1. 1.School of Mathematics and Computer ScienceGuizhou Normal CollegeGuiyang, GuizhouChina
  2. 2.Department of MathematicsGuizhou UniversityGuiyang, GuizhouChina
  3. 3.Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and InformaticsComenius UniversityBratislavaSlovakia
  4. 4.Mathematical InstituteSlovak Academy of SciencesBratislavaSlovakia
  5. 5.Department of MathematicsXiangtan UniversityXiangtan, HunanChina

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