Maxwell’s three-dimensional viscoelastic model for fractal medium

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Real media and materials have structural peculiarities and faults at different scale levels. Thus, fractal
structures may be a model for such media. Fractal properties effect medium fields of stress and strain. In
classical linear reological models the fields of stress and strain have exponential solution. In the present paper
a Maxwell’s three-dimensional viscoelastic model for fractal medium is considered. One of the appropriate
mathematical methods for modelling media with fractal properties is fractional differentiation. Maxwell’s three-
dimensional viscoelastic model is presented with Caputo’s derivative. It is shown that depending on a fractional
differentiation paramete the law of stress feild relaxation will consider medium fractal properties.
The consiered reological model may be compared with experimental geoacoustic emission intensity observed
in sedimentary rocks. The characteristics of geioacoustic emission give an opportunity to receive the information
on medium stress state.