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Applications of generalized fixed points theorems to the existence of uncertainly hyperbolic partial differential equations with finite delay

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Abstract

We study the existence and uniqueness of solutions for a boundary value problem associated with a class of fuzzy hyperbolic partial differential equations with finite delay. We establish a more general definition of integral solutions for the boundary value problem and, using some results of fixed point of weakly contractive mappings on partially ordered metric spaces, we prove that the existence of just a lower or an upper solution is enough to prove the existence and uniqueness of fuzzy solutions in the setting of a generalized Hukuhara derivative. Our existence results generalize, extend, and improve different results existing in the literature about this problem.

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Acknowledgements

The authors would like to thank the referees for their helpful comments and valuable suggestions, which have greatly improved the paper. The second author has been support by project UTA-Mayor 4757-21 and the third author has been supported by Vicerrectoría de Investigación y Extensión of Universidad Industrial de Santander.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad Nacional de Colombia - Sede Orinoquia, Kilómetro 9 vía a Caño Limón, Arauca, Colombia

    Vladimir Angulo-Castillo

  2. Departamento de Matemática, Universidad de Tarapacá, Casilla 7D, Arica, Chile

    Y. Chalco-Cano

  3. Universidad Industrial de Santander, Escuela de Matemáticas, A.A.678, Bucaramanga, Colombia

    Élder J. Villamizar-Roa

Authors
  1. Vladimir Angulo-Castillo
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  2. Y. Chalco-Cano
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  3. Élder J. Villamizar-Roa
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Correspondence to Y. Chalco-Cano.

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Communicated by Jose Alberto Cuminato.

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Angulo-Castillo, V., Chalco-Cano, Y. & Villamizar-Roa, É.J. Applications of generalized fixed points theorems to the existence of uncertainly hyperbolic partial differential equations with finite delay. Comp. Appl. Math. 41, 182 (2022). https://doi.org/10.1007/s40314-022-01855-w

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  • DOI: https://doi.org/10.1007/s40314-022-01855-w

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