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.

From Differences to Derivatives

A relation showing that the Grünwald-Letnikov and generalized Cauchy derivatives are equal is deduced confirming the validity of a well known conjecture. Integral representations for both direct and reverse fractional differences are presented. From these the fractional derivative is readily obtained generalizing the Cauchy integral formula.

Fractional Derivatives and Fractional Powers as Tools in Understanding Wentzell Boundary Value Problems for Pseudo-Differential Operators Generating Markov Processes

Mathematics Subject Classification: 26A33, 31C25, 35S99, 47D07.

On Multidimensional Analogue of Marchaud Formula for Fractional Riesz-Type Derivatives in Domains in R^n

2000 Mathematics Subject Classification: 26A33, 42B20

Comparative Analysis of Viscoelastic Models Involving Fractional Derivatives of Different Orders

Mathematics Subject Classification: 74D05, 26A33

On the Equivalence of the Riemann-Liouville and the Caputo Fractional Order Derivatives in Modeling of Linear Viscoelastic Materials

Mathematics Subject Classification: 26A33

On a Differential Equation with Left and Right Fractional Derivatives

Mathematics Subject Classification: 26A33; 70H03, 70H25, 70S05; 49S05

Caputo Derivatives in Viscoelasticity: A Non-Linear Finite-Deformation Theory for Tissue

Mathematics Subject Classification: 26A33, 74B20, 74D10, 74L15

Time-Fractional Derivatives in Relaxation Processes: A Tutorial Survey

2000 Mathematics Subject Classification: 26A33, 33E12, 33C60, 44A10, 45K05, 74D05,

Well-Posedness of Diffusion-Wave Problem with Arbitrary Finite Number of Time Fractional Derivatives in Sobolev Spaces H^s

Mathematics Subject Classification 2010: 26A33, 33E12, 35S10, 45K05.

Hamilton’s Principle with Variable Order Fractional Derivatives

MSC 2010: 26A33, 70H25, 46F12, 34K37 Dedicated to 80-th birthday of Prof. Rudolf Gorenflo

Fractional Derivatives in Spaces of Generalized Functions

MSC 2010: 26A33, 46Fxx, 58C05 Dedicated to 80-th birthday of Prof. Rudolf Gorenflo

On Arrangements of Real Roots of a Real Polynomial and Its Derivatives

2000 Mathematics Subject Classification: 12D10.

On Root Arrangements of Polynomial-Like Functions and their Derivatives

2000 Mathematics Subject Classification: 12D10.

Large and Moderate Deviations Principles for Recursive Kernel Estimator of a Multivariate Density and its Partial Derivatives

2000 Mathematics Subject Classification: 62G07, 60F10.