Fractional trajectories: Decorrelation versus friction Report Title The fundamental connection between fractional calculus and subordination processes is explored and affords a physical interpretation of a fractional trajectory, that being an average over an ensemble of stochastic trajectories. Heretofore what has been interpreted as intrinsic friction, a form of non-Markovian dissipation that ...

In this paper a fractional order PI controller (FOPI) is proposed for the speed control of Permanent Magnet Synchronous Motor(PMSM). Fractional calculus is introduced into the PI controller, and proposes a robust fractional order PI controller (FOPI) for the speed control of a PMSM .PMSM drive system is a nonlinear system which is sensitive to load disturbance, parameter variation, unmodelled a...

Non-local kinetic problems spanning a wide area of where fractional calculus is applicable have been analyzed. Classical kinetics based on the Continuum Time Random Walk diffusion model with absence stationary states, real-world from pharmacokinetics, and modern material processing reviewed. Fractional allometry has considered potential application. The main focus in analysis paid to memory fun...

It has been recognized recently that fractional calculus is useful for handling scaling structures and processes. We begin this survey by pointing out the relevance of the subject to physical situations. Then the essential definitions and formulae from fractional calculus are summarized and their immediate use in the study of scaling in physical systems is given. This is followed by a brief sum...

The subject of fractional calculus addresses the research asserted derivatives and integrations over complex domains their utilization [...]

The study aims to prove the controllability of mild solution for semilinar fractional integerodifferential equations with nonlocal conditions in banach spaces.
 Fractional calculus, compact semigroups and fixed point theorem, are concepts consulted obtain results this work.

In this work, the vibrations of viscoelastic functionally graded Euler–Bernoulli nanostructure beams are investigated using the fractional-order calculus. It is assumed that the functionally graded nanobeam (FGN) is due to a periodic heat flux. FGN can be considered as nonhomogenous composite structures; with continuous structural changes along the thick- ness of the nanobeam usually, it change...

In this paper we discuss the fractional extention of classical Lagrangian and Hamiltonian mechanics. We give a view of the mathematical tools associated with fractional calculus as well as a description of some applications.