Arabian Journal of Mathematics

, Volume 8, Issue 2, pp 79–94 | Cite as

Boundedness and power-type decay of solutions for a class of generalized fractional Langevin equations

  • Ahmad M. AhmadEmail author
  • Khaled M. Furati
  • Nasser-Eddine Tatar
Open Access


In this paper we study the long-time behavior of solutions for a general class of Langevin-type fractional integro-differential equations. The involved fractional derivatives are either of Riemann–Liouville or Caputo type. Reasonable sufficient conditions under which the solutions are bounded or decay like power functions are established. For this purpose, we combine and generalize some well-known integral inequalities with some crucial estimates. Our findings are supported by examples and special cases.

Mathematics Subject Classification

34A08 34A12 34C11 



The authors would like to acknowledge the support provided by King Fahd University of Petroleum and Minerals (KFUPM) through project No. IN161010.


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Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  • Ahmad M. Ahmad
    • 1
    Email author
  • Khaled M. Furati
    • 1
  • Nasser-Eddine Tatar
    • 1
  1. 1.Department of Mathematics and StatisticsKing Fahd University of Petroleum and MineralsDhahranSaudi Arabia

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