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...

In this paper, a novel image denoising algorithm named fractional integral image denoising algorithm (FIIDA) is proposed, which based on fractional calculus Riemann-Liouville definition. The structures of n*n fractional integral masks of this algorithm on the directions of 135 degrees, 90 degrees, 45 degrees, 0 degrees, 180 degrees, 315 degrees, 270 degrees and 225 degrees are constructed and d...

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 fundamental solution of the fractional diffusion equation of distributed order in time (usually adopted for modelling sub-diffusion processes) is obtained based on its Mellin-Barnes integral representation. Such solution is proved to be related via a Laplace-type integral to the Fox-Wright functions. A series expansion is also provided in order to point out the distribution of time-scales r...

In this paper, a novel digital image denoising algorithm called generalized fractional integral filter is introduced based on the generalized Srivastava-Owa fractional integral operator. The structures of n×n fractional masks of this algorithm are constructed. The denoising performance is measured by employing experiments according to visual perception and PSNR values. The results demonstrate t...

In this paper, we investigate four different types of Ulam stability, i.e., Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-Hyers-Rassias stability for a class of nonlinear implicit fractional differential equations with non-instantaneous integral impulses and nonlinear integral boundary condition. We also establish certain conditions fo...

Stable non-Gaussian self-similar mixed moving averages can be decomposed into several components. Two of these are the periodic and cyclic fractional stable motions which are the subject of this study. We focus on the structure of their integral representations and show that the periodic fractional stable motions have, in fact, a canonical representation. We study several examples and discuss q...

Stable non-Gaussian self-similar mixed moving averages can be decomposed into several components. Two of these are the periodic and cyclic fractional stable motions which are the subject of this study. We focus on the structure of their integral representations and show that the periodic fractional stable motions have, in fact, a canonical representation. We study several examples and discuss q...

This work focuses on a new type of cost function based on fractional operators. To do so, the concept of definite integral is extended to arbitrary real-order. Some properties of this new fractional-order definite integral are studied and a fractional-order Barrow’s rule is proposed. It is illustrated by an example (the design of an IIR filter) how this new kind of cost function can be a valuab...