In this paper, we prove the existence of global weak solutions for a model described
by the fractional Heisenberg equation for the magnetization field and the viscoelastic
integro-differential equation for the displacements. We study the three-dimensional
case. The demonstration of the existence of weak solution is based on the method of
Faedo-Galerkin; and to get the convergence of the nonlinear terms, we introduce the
commutator structure.

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• Global existence of weak solutions to a three-dimensional fractional model in magneto-viscoelastic interactions