In order to improve the correlation accuracy of correlation algorithm, the fractional order correlation algorithm of uncertain time sequences is proposed in this paper. By taking advantage of the memory property of fractional order, the algorithm introduces the measurement of fractional order differential for the local trend of time sequence into the correlation algorithm and also analyzes the ...

The fractional Boltzmann equation for resonance radiation transport in plasma is proposed. We start from the standard Boltzmann equation, averaging over frequencies leads to appearance of fractional derivative. This fact is in accordance with the conception of latent variables leading to hereditary and non-local dynamics (in particular, fractional dynamics). The presence of the fractional mater...

We propose a systematical approach to construct generic fractional quantum anomalous Hall states, which are generalizations of the fractional quantum Hall states to lattice models with zero net magnetic field and full lattice translation symmetry. Local and translationally invariant Hamiltonians can also be constructed, for which the proposed states are unique ground states. Our result demonstr...

One of the ongoing issues with fractional-order diffusion models is the design of efficient numerical schemes for the space and time discretizations. Until now, most models have relied on a low-order finite difference method to discretize both the fractional-order space and time derivatives. While the finite difference method is simple and straightforward to solve integer-order differential equ...

In this paper we present the methods of Quasilinearization and Generalized Quasilinearization for hybrid Caputo fractional differential equations which are Caputo fractional differential equations with fixed moments of impulse. In order to prove this results we use the weakened assumption of -continuity in place of local Hölder continuity.

By using a new bilinear estimate, a pointwise estimate of the generalized Oseen kernel and an idea of fractional bootstrap, we establish optimal local smoothing and decay estimates of solutions to the Navier-Stokes equations with fractional dissipation. We also show that solutions are analytic in space variables.