Received (Day Month Year) Revised (Day Month Year) Communicated by (xxxxxxxxxx) Fractional B-splines are a natural extension of classical B-splines. In this short paper, we show their relations to fractional divided differences and fractional difference operators , and present a generalized Hermite-Genochi formula. This formula then allows the definition of a larger class of fractional B-splines.

Texture enhancement is one of the most important techniques in digital image processing and plays an essential role in medical imaging since textures discriminate information. Most image texture enhancement techniques use classical integral order differential mask operators or fractional differential mask operators using fixed fractional order. These masks can produce excessive enhancement of l...

Texture enhancement for medical images is the most important technique in medical image diagnosis. This paper introduces a texture enhancement technique for medical images by using fractional differential (FD) masks based on Srivastava-Owa fractional operators. We also construct a 2D isotropic gradient mask based on generalized fractional operators. Texture enhancement performance is measured b...

In the paper, we present some applications and features related with the new notions of fractional derivatives with a time exponential kernel and with spatial Gauss kernel for gradient and Laplacian operators. Specifically, for these new models we have proved the coherence with the thermodynamic laws. Hence, we have revised the standard linear solid of Zener within continuum mechanics and the m...

Let dγ(x) ≡ πe 2 dx for all x ∈ R be the Gauss measure on R. In this paper, the authors establish the characterizations of the space BMO(γ) of Mauceri and Meda via commutators of either local fractional integral operators or local fractional maximal operators. To this end, the authors first prove that such a local fractional integral operator of order β is bounded from L(γ) to L(γ), or from the...

Cable equations with fractional order temporal operators are introduced to model electrotonic properties of spiny neuronal dendrites. These equations are derived from Nernst-Planck equations with fractional order operators to model the anomalous subdiffusion that arises from trapping properties of dendritic spines. The fractional cable models predict that postsynaptic potentials propagating alo...

This paper is devoted to the study of four integral operators that are basic generalizations and modifications of fractional integrals of Hadamard, in the space X c of Lebesgue measurable functions f on R+ = (0,∞) such that ∞ ∫ 0 ∣∣ucf (u)∣∣p du u <∞ (1 p <∞), ess sup u>0 [ u ∣∣f (u)∣∣]<∞ (p =∞), for c ∈ R = (−∞,∞), in particular in the space Lp(0,∞) (1 p ∞). Formulas for the Mellin transforms ...

The object of the present paper is to derive various distortion theorems for fractional calculus and fractional integral operators of functions in the class BT(j, λ, α) consisting of analytic and univalent functions with negative coefficients. Furthermore, some of integral operators of functions in the class BT(j, λ, α) is shown. 2000 Mathematics Subject Classification: 30C45. 1.Introduction an...

Based on the weighted and shifted Grünwald difference (WSGD) operators [24], we further construct the compact finite difference discretizations for the fractional operators. Then the discretization schemes are used to approximate the one and two dimensional space fractional diffusion equations. The detailed numerical stability and error analysis are theoretically performed. We theoretically pro...

In this paper, we applied a new analytical geometrical method which so called fractal index method to find a new solution of the generalized fractional Riccati equation of arbitrary order, we also wrote the solution on the closed form as an infinte series and showed that the series is convergent within some closed disk. The fractional operators are taken in sense of the Riemann-Liouville operat...