In this paper, we present a new fractional dynamical theory, i.e., the dynamics of a Birkhoffian system with fractional derivatives (the fractional Birkhoffian mechanics), which gives a general method for constructing a fractional dynamical model of the actual problem. By using the definition of...
The fractional Liouville equation is obtained\nfrom the conservation of probability to find a system in a fractional volume\nelement. This equation is used to obtain Bogoliubov hierarchy and fractional\nkinetic equations with fractional derivatives. Statistical mechanics of\nfractional generalization of ...
It appears that equations of motion in the noncommutative framework do not mix left and right derivatives thus being simple to solve at least in the linear case. As an example, two models of oscillator with fractional derivatives are studied....
Katugampola [e-printarXiv:1410.6535] recently introduced a limit based fractional derivative,Dα(referred to in this work as the Katugampola fractional derivative) that maintains many of the familiar properties of standard derivatives such as the product, quotient, and chain rules. Typically, fractio...
In the representations the integration over velocities is not restricted by any boundary conditions; matrices, which have to be inverted in course of doing Gaussian integrals, do not contain any derivatives in time, and spinor and isospinor structures of the propagators are given explicitly. One...
Response spectral density determination for nonlinear systems endowed with fractional derivatives and subject to colored noise Fan Kong, Pol D. Spanos January 2020 Article 103023 select article On the usefulness of gradient information in surrogate modeling: Application to uncertainty propagation in composite...
Features of fractional operators involving fractional derivatives and their applications to the problems of mechanics of solids The given Chapter consists of Introduction, 8 paragraphs and Conclusion. The state of the art review of papers devoted to the fractional derivatives, fract... YA Rossikhin,MV...
Fractional Derivatives for Physicists and Engineers: Volume I Background and Theory Volume II Applications The first derivative of a particle coordinate means its velocity, the second means its acceleration, but what does a fractional order derivative mean? Where does it come from, how does it ...
Description of the Impulse Response in Rods by Fractional Derivatives ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und MechanikI. Scha¨fer and H.-J. Seifert, Description of ... I. Schfer Dipl.-Ing. and,HJ Seifert - ZAMM - Journal of Applied ...
We elaborate fractional geometric models of physical interactions and we formulate a method of nonholonomic deformations to other types of fractional derivatives. The main result of this paper consists of a proof that, for corresponding classes of nonholonomic distributions, a large class of physical ...