On the ($$\alpha $$,$$\beta $$)-Scott–Blair anti-Zener arrangement

Abstract

In this paper, we study some fractional rheological anti-Zener equations that are derived from the ordinary anti-Zener model. We analyze three situations : the theoretical anti-Zener, the $$\alpha $$-Scott–Blair anti-Zener and the $$(\alpha ,\beta )$$-Scott–Blair anti-Zener models. The Mellin transform technique and Fox-H functions are investigated to derive relaxation modulus and the creep compliance function corresponding to each model. The limit cases are discussed.