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

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.