On the Mellin Transforms of Dirac’S Delta Function, The Hausdorff Dimension Function, and The Theorem by Mellin

Mathematics Subject Classification: 44A05, 46F12, 28A78

Generalization of the Modified Bessel Function and Its Generating Function

2000 Mathematics Subject Classification: 33C10, 33-02, 60K25

On the Generalized Confluent Hypergeometric Function and Its Application

2000 Mathematics Subject Classification: 26A33, 33C20

An Expansion Formula for Fractional Derivatives and its Application

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