1205.5343 (Teodor M. Atanackovic et al.)

On a system of equations arising in viscoelasticity theory of fractional
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Teodor M. Atanackovic, Stevan Pilipovic, Dusan Zorica

We study a system of partial differential equations with integer and fractional derivatives arising in the study of forced oscillatory motion of a viscoelastic rod. We propose a new approach considering a quotient of relations appearing in the constitutive equation instead the constitutive equation itself. Both, a rod and a body are assumed to have finite mass. The motion of a body is assumed to be translatory. Existence and uniqueness for the corresponding initial-boundary value problem is proved within the spaces of functions and distributions.

View original: http://arxiv.org/abs/1205.5343