In this paper, we extend the recently introduced concept of fractional wavelet transform to obtain directional subbands of an image. Fractional wavelet decomposition is based on two-channel unbalanced lifting structures whereby it is possible to decompose a given discretetime signal x[n] sampled with period T into two sub-signals x1[n] and x2[n] whose average sampling periods are pT and qT , re...

The generalized diffusion equations with fractional order derivatives have shown be quite efficient to describe the diffusion in complex systems, with the advantage of producing exact expressions for the underlying diffusive properties. Recently, researchers have proposed different fractional-time operators (namely: the Caputo-Fabrizio and Atangana-Baleanu) which, differently from the well-know...

‎it is commonly accepted that fractional differential equations play‎ ‎an important role in the explanation of many physical phenomena‎. ‎for‎ ‎this reason we need a reliable and efficient technique for the‎ ‎solution of fractional differential equations‎. ‎this paper deals with‎ ‎the numerical solution of a class of fractional differential‎ ‎equation‎. ‎the fractional derivatives are described...

Fractional-step methods are a popular and powerful divide-and-conquer approach for the numerical solution of differential equations. When integrators fractional steps Runge--Kutta methods, such can be written as generalized additive (GARK) thus representation analysis done through GARK framework. We show how general Butcher tableau linear stability related to coefficients splitting method, indi...

We present data from a sample of 190 healthy adults including assessments of 4 cognitive factor scores, 12 cognitive tests, and 115 MRI-assessed neuroanatomical variables (cortical thicknesses, cortical and sub-cortical volumes, fractional anisotropy, and radial diffusivity). These data were used in estimating underlying sources of individual variation via independent component analysis (Watson...

We show that every (sub)cubic n-vertex graph with sufficiently large girth has fractional chromatic number at most 2.2978 which implies that it contains an independent set of size at least 0.4352n. Our bound on the independence number is valid to random cubic graphs as well as it improves existing lower bounds on the maximum cut in cubic graphs with large girth.

We consider stochastic flow on Rn driven by fractional Brownian motion with Hurst parameter H ∈ ( 1 2 , 1), and study tangent flow and the growth of the Hausdorff measure of sub-manifolds of Rn as they evolve under the flow. The main result is a bound on the rate of (global) growth in terms of the (local) Hölder norm of the flow.

We consider stochastic flow on Rn driven by fractional Brownian motion with Hurst parameter H ∈ ( 1 2 , 1), and study tangent flow and the growth of the Hausdorff measure of sub-manifolds of Rn as they evolve under the flow. The main result is a bound on the rate of (global) growth in terms of the (local) Hölder norm of the flow.

in this article, we survey the asymptotic stability analysis of fractional differential systems with the prabhakar fractional derivatives. we present the stability regions for these types of fractional differential systems. a brief comparison with the stability aspects of fractional differential systems in the sense of riemann-liouville fractional derivatives is also given.

In this work, we consider a sub-diffusion functional differential equation with an integral condition. We apply the method of semidiscretization in time, to establish the existence and uniqueness of solutions. We also study the continuation of the solution to the maximal interval of existence. By using Rothe’s sequence and values of the fractional integrals over time steps, the results are obta...