Fractal and Fractional (Jun 2023)

On a Singular Non local Fractional System Describing a Generalized Timoshenko System with Two Frictional Damping Terms

  • Said Mesloub,
  • Reem K. Alhefthi

DOI
https://doi.org/10.3390/fractalfract7070514
Journal volume & issue
Vol. 7, no. 7
p. 514

Abstract

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This paper concerns a nonhomogeneous singular fractional order system, with two frictional damping terms. This system can be considered as a generalization of the so-called Timoshenko system. Results on the existence, uniqueness, and continuous dependence on the solution were obtained via an energy approach, which mainly relies on a priori bounds and density arguments. The approach relies on functional analysis tools and operator theory. Very few results concerning the well-posedness of fractional order Timoshenko systems can be found in the literature. Our results generalize and improve the previous ones and significantly boost the development of the used method.

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