An Expansion Formula for Fractional Derivatives and its Application

Abstract

An expansion formula for fractional derivatives given as in form of a\nseries involving function and moments of its k-th derivative is derived. The\nconvergence of the series is proved and an estimate of the reminder is given.\nThe form of the fractional derivative given here is especially suitable in\nderiving restrictions, in a form of internal variable theory, following from\nthe second law of thermodynamics, when applied to linear viscoelasticity of\nfractional derivative type.