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Hyers-Ulam and Hyers-Ulam-Rassias Stability for a Class of Integro-Differential Equations

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Mathematical Methods in Engineering

Part of the book series: Nonlinear Systems and Complexity ((NSCH,volume 23))

Abstract

We analyse different kinds of stabilities for a class of very general nonlinear integro-differential equations of Volterra type within appropriate metric spaces. Sufficient conditions are obtained in view to guarantee Hyers-Ulam stability and Hyers-Ulam-Rassias stability for such a class of integro-differential equations. We will consider the different situations of having the integrals defined on finite and infinite intervals. Among the used techniques, we have fixed point arguments and generalizations of the Bielecki metric. Concrete examples will be also described in view to illustrate the obtained results.

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Acknowledgements

This work was supported in part by FCT–Portuguese Foundation for Science and Technology through the Center for Research and Development in Mathematics and Applications (CIDMA) of University of Aveiro, within UID/MAT/04106/2013, and through the Center of Mathematics and Applications of University of Beira Interior (CMA-UBI), within project UID/MAT/00212/2013.

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Authors and Affiliations

  1. Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, Aveiro, Portugal

    L. P. Castro

  2. Center of Mathematics and Applications of University of Beira Interior (CMA-UBI), Department of Mathematics, University of Beira Interior, Covilhã, Portugal

    A. M. Simões

Authors
  1. L. P. Castro
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  2. A. M. Simões
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Correspondence to A. M. Simões .

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Editors and Affiliations

  1. Department of Mathematics, Çankaya University, Ankara, Turkey

    Kenan Taş

  2. Department of Mathematics, Çankaya University, Ankara, Turkey

    Dumitru Baleanu

  3. Instituto Superior de Engenharia do Porto, Porto, Portugal

    J. A. Tenreiro Machado

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Castro, L.P., Simões, A.M. (2019). Hyers-Ulam and Hyers-Ulam-Rassias Stability for a Class of Integro-Differential Equations. In: Taş, K., Baleanu, D., Machado, J. (eds) Mathematical Methods in Engineering. Nonlinear Systems and Complexity, vol 23. Springer, Cham. https://doi.org/10.1007/978-3-319-91065-9_3

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  • DOI: https://doi.org/10.1007/978-3-319-91065-9_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-91064-2

  • Online ISBN: 978-3-319-91065-9

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