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Bounded Solutions of Functional Integro-Differential Equations Arising from Heat Conduction in Materials with Memory

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Abstract

In this paper, we consider recurrent behavior of bounded solutions for a functional integro-differential equation arising from heat conduction in materials with memory. Prior to the main results, we give a new version of composite theorem on measure pseudo almost automorphic functions involved in delay. Based on recently obtained results on the uniform exponential stability as well as contraction mapping principle, we prove some existence and uniqueness theorems on the recurrence of bounded mild solutions for the addressed equations with infinite delay. Finally, we finish this paper with an example on partial integro-differential equation which frequently comes to light in the study of heat conduction.

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Authors and Affiliations

  1. Xidian University, Shaanxi, China

    Y.-K. Chang

  2. Prince Sultan University, Riyadh, Saudi Arabia

    J. Alzabut

  3. Universidad de Talca, Talca, Chile

    R. Ponce

Authors
  1. Y.-K. Chang
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  2. J. Alzabut
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  3. R. Ponce
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Correspondence to Y.-K. Chang.

Additional information

Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 178, Optimal Control, 2020.

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Chang, YK., Alzabut, J. & Ponce, R. Bounded Solutions of Functional Integro-Differential Equations Arising from Heat Conduction in Materials with Memory. J Math Sci 276, 237–252 (2023). https://doi.org/10.1007/s10958-023-06738-x

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