A note on fractional derivatives and fractional powers of operators

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 )

Fractional Powers of Derivatives in Classical Mechanics

Fractional analysis is applied to describe classical dynamical systems. Fractional derivative can be defined as a fractional power of derivative. The infinitesimal generators {H, ·} and L = G(q, p)∂q + F (q, p)∂p, which are used in equations of motion, are derivative operators. We consider fractional derivatives on a set of classical observables as fractional powers of derivative operators. As ...

Fractional Powers of Operators of Tsallis Ensemble and their Parameter

From this he went on to obtain several other identities in elegant ways which are all central in the development of quantum time evolution, Gibbsian ensembles in equilibrium quantum statistical mechanics, perturbation expansions, inequalities concerning correlation functions etc., all of which depend on the appearance of the exponential operator of the form introduced in Eq.(1). For a comprehen...

On the Sum of Fractional Derivatives and M-accretive Operators

Domination number of graph fractional powers

For any $k in mathbb{N}$, the $k$-subdivision of graph $G$ is a simple graph $G^{frac{1}{k}}$, which is constructed by replacing each edge of $G$ with a path of length $k$. In [Moharram N. Iradmusa, On colorings of graph fractional powers, Discrete Math., (310) 2010, No. 10-11, 1551-1556] the $m$th power of the $n$-subdivision of $G$ has been introduced as a fractional power of $G$, denoted by ...