Local Fractional Derivatives of Differentiable Functions are Integer-order Derivatives or Zero

A Note on Fractional Order Derivatives and Table of Fractional Derivatives of Some Special Functions

and Applied Analysis 3 Ta bl e 1: Fr ac tio na lo rd er de riv at iv es fo rs om ef un ct io ns . Fu nc tio ns Lfr ac tio na ld er iv at iv es x β , > − 1 x − α + β Γ ( 1 + β )

Properties of Fractional Order Derivatives for Groups of Relations/Functions

The concept of fractional order derivative can be found in extensive range of many different subject areas. For this reason, the concept of fractional order derivative should be examined. After giving different methods mostly used in engineering and scientific applications, the omissions or errors of these methods will be discussed in this study. The mostly used methods are Euler, Riemann-Liouv...

Rings of functions with integer derivatives at x=1

Relative widths of smooth functions determined by fractional order derivatives

For two subsetsW and V of a normed space X. The relative Kolmogorov n-width ofW relative to V in X is defined by Kn(W,V )X := inf Ln sup f∈W inf g∈V∩Ln ‖f − g‖X , where the infimum is taken over all n-dimensional subspaces Ln of X. For ∈ R+, defineW p (1 p ∞) to be the collection of 2 -periodic and continuous functions f representable as a convolution f (t)= c + (B ∗ g)(t), where g ∈ Lp(T ), T ...

Discrete-Time Fractional Differentiation from Integer Derivatives

Discrete-time fractional derivative filters (1-D and 2-D) are shown to be well approximated from a small set of integer derivatives. A fractional derivative of arbitrary order (and, in 2-D, of arbitrary orientation) can therefore be efficiently computed from a linear combination of integer derivatives of the underlying signal or image.