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Asymptotic Behavior of Solutions for a Class of Fractional Integro-differential Equations

  • Ahmad M. Ahmad
  • Khaled M. Furati
  • Nasser-Eddine Tatar
Article

Abstract

In this paper, we study the asymptotic behavior of solutions for a general class of fractional integro-differential equations. We consider the Caputo fractional derivative. Reasonable sufficient conditions under which the solutions behave like power functions at infinity are established. For this purpose, we use and generalize some well-known integral inequalities. It was found that the solutions behave like the solutions of the associated linear differential equation with zero right hand side. Our findings are supported by examples.

Keywords

Asymptotic behavior fractional integro-differential equation Caputo fractional derivative integral inequalities nonlocal source 

Mathematics Subject Classification

34A08 35B40 26D10 

Notes

Acknowledgements

The authors would like to acknowledge the support provided by King Fahd University of Petroleum and Minerals (KFUPM) through project number IN161010.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Ahmad M. Ahmad
    • 1
  • 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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