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On the Weak Solvability of a Fractional Viscoelasticity Model

Abstract

The existence of a weak solution of a boundary value problem for a fractional viscoelasticity model that is a fractional analogue of the anti-Zener model with memory along trajectories of motion is proved. The rheological equation of the given model involves fractional-order derivatives. The proof relies on an approximation of the original problem by a sequence of regularized ones and on the theory of regular Lagrangian flows.

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Correspondence to V. G. Zvyagin.

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Original Russian Text © V.G. Zvyagin, V.P. Orlov, 2018, published in Doklady Akademii Nauk, 2018, Vol. 483, No. 2.

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Zvyagin, V.G., Orlov, V.P. On the Weak Solvability of a Fractional Viscoelasticity Model. Dokl. Math. 98, 568–570 (2018). https://doi.org/10.1134/S1064562418070104

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  • DOI: https://doi.org/10.1134/S1064562418070104