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Inverse Problems for Degenerate Fractional Integro-Differential Equations

Author

Listed:
  • Mohammed Al Horani

    (Department of Mathematics, The University of Jordan, Amman 11942, Jordan)

  • Mauro Fabrizio

    (Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato 5, 40126 Bologna, Italy)

  • Angelo Favini

    (Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato 5, 40126 Bologna, Italy)

  • Hiroki Tanabe

    (Takarazuka, Hirai Sanso 12-13, Osaka 665-0817, Japan)

Abstract

This paper deals with inverse problems related to degenerate fractional integro-differential equations in Banach spaces. We study existence, uniqueness and regularity of solutions to the problem, claiming to extend well known studies for the case of non-fractional equations. Our method is based on transforming the inverse problem to a direct problem and identifying the conditions under which this direct problem has a unique solution. The conditions under which the unique strict solution can be compared with the case of a mild solution, obtained in previous studies under quite restrictive requirements, are on the underlying functions. Applications from partial differential equations are given to illustrate our abstract results.

Suggested Citation

  • Mohammed Al Horani & Mauro Fabrizio & Angelo Favini & Hiroki Tanabe, 2020. "Inverse Problems for Degenerate Fractional Integro-Differential Equations," Mathematics, MDPI, vol. 8(4), pages 1-11, April.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:532-:d:341305
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    References listed on IDEAS

    as
    1. M. AL Horani & A. Favini, 2006. "An Identification Problem for First-Order Degenerate Differential Equations," Journal of Optimization Theory and Applications, Springer, vol. 130(1), pages 41-60, July.
    2. Alberto Favaron & Angelo Favini, 2013. "On the Behaviour of Singular Semigroups in Intermediate and Interpolation Spaces and Its Applications to Maximal Regularity for Degenerate Integro-Differential Evolution Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-37, December.
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    Cited by:

    1. Ekaterina Gribanova, 2022. "Elaboration of an Algorithm for Solving Hierarchical Inverse Problems in Applied Economics," Mathematics, MDPI, vol. 10(15), pages 1-19, August.

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    1. M. Al Horani & A. Favini & A. Lorenzi, 2009. "Second-Order Degenerate Identification Differential Problems," Journal of Optimization Theory and Applications, Springer, vol. 141(1), pages 13-36, April.
    2. Mohammed Al Horani & Angelo Favini, 2015. "Perturbation Method for First- and Complete Second-Order Differential Equations," Journal of Optimization Theory and Applications, Springer, vol. 166(3), pages 949-967, September.

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