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Relaxation modulus and creep compliance corresponding to fractionalanti-Zener and Zener models are calculated and restrictions on model parametersnarrowing thermodynamical constraints are posed in order to ensure relaxationmodulus and creep compliance to be completely monotone and Bernstein functionrespectively, that a priori guarantee the positivity of stored energy anddissipated power per unit volume, derived in time domain by considering thepower per unit volume. Both relaxation modulus and creep compliance for modelparameters obeying thermodynamical constraints, proved that can also beoscillatory functions with decreasing amplitude. Model used in numericalexamples of relaxation modulus and creep compliance is also analyzed for theasymptotic behavior near the initial time instant and for large time.

Energy balance for fractional anti-Zener and Zener models in terms of relaxation modulus and creep compliance