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

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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.

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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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Authors and Affiliations

  1. Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia

    Ahmad M. Ahmad, Khaled M. Furati & Nasser-Eddine Tatar

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  1. Ahmad M. Ahmad
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  2. Khaled M. Furati
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  3. Nasser-Eddine Tatar
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Correspondence to Ahmad M. Ahmad.

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Ahmad, A.M., Furati, K.M. & Tatar, NE. Asymptotic Behavior of Solutions for a Class of Fractional Integro-differential Equations. Mediterr. J. Math. 15, 188 (2018). https://doi.org/10.1007/s00009-018-1235-4

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  • DOI: https://doi.org/10.1007/s00009-018-1235-4

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