Related papers: Fractional Differentiation Operator over an Infini…
The notion of a local fractional derivative (LFD) was introduced recently for functions of a single variable. LFD was shown to be useful in studying fractional differentiability properties of fractal and multifractal functions. It was…
It is an established fact that a finite difference operator approximates a derivative with a fixed algebraic rate of convergence. Nevertheless, we exhibit a new finite difference operator and prove it has spectral accuracy. Its rate of…
We introduce a notion of fractional Laplacian for functions which grow more than linearly at infinity. In such case, the operator is not defined in the classical sense: nevertheless, we can give an ad-hoc definition which can be useful for…
The fractional calculus of variations is now a subject under strong research. Different definitions for fractional derivatives and integrals are used, depending on the purpose under study. In this paper the fractional operators are defined…
In this paper, a new fractional operator of variable order with the use of the monotonic increasing function is proposed in sense of Caputo type. The properties in term of the Laplace and Fourier transforms are analyzed and the results for…
Fractional equations have become the model of choice in several applications where heterogeneities at the microstructure result in anomalous diffusive behavior at the macroscale. In this work we introduce a new fractional operator…
In this paper we introduce Lipschitz spaces with respect to the Gaussian measure, and study the boundedness of the fractional integral and fractional derivative operators on them.The methods are general enough to provide alternative proofs…
In this paper we study the regularity properties of fractional maximal operators acting on $BV$-functions. We establish new bounds for the derivative of the fractional maximal function, both in the continuous and in the discrete settings.
For $\alpha\geq 2$, we investigate a class of Fourier extension operators on fractional surfaces $(\xi,|\xi|^\alpha)$. For the corresponding $\alpha$-Strichartz inequalities, by applying the missing mass method and bilinear restriction…
Diffusive representations of fractional differential and integral operators can provide a convenient means to construct efficient numerical algorithms for their approximate evaluation. In the current literature, many different variants of…
Local fractional derivative and integrals are revealed as one of useful tools to deal with everywhere continuous but nowhere differentiable functions in fractal areas ranging from fundamental science to engineering. In this paper, a…
Fractional difference operators possess nonlocal structure which largely affects and complicates the qualitative analysis of fractional difference equations. In this article, we discuss the effect of this memory property on asymptotic…
Some mathematical models of applied problems lead to the need of solving boundary value problems with a fractional power of an elliptic operator. In a number of works, approximations of such a nonlocal operator are constructed on the basis…
We introduce the notion of structural derivative on time scales. The new operator of differentiation unifies the concepts of fractal and fractional order derivative and is motivated by lack of classical differentiability of some…
In this article, we impose a new class of fractional analytic functions in the open unit disk. By considering this class, we define a fractional operator, which is generalized Salagean and Ruscheweyh differential operators. Moreover, by…
We introduce two kinds of fractional integral operators; the one is defined via the exponential-integral function $$ E_1(x)=\int_x^\infty \frac{e^{-t}}{t}\,dt,\quad x>0, $$ and the other is defined via the special function $$…
A general framework to construct fractal interpolation surfaces (FISs) on rectangular grids was presented and bilinear FIS was deduced by Ruan and Xu [Bull. Aust. Math. Soc. 91(3), 2015, pp. 435-446]. From the view point of operator theory…
In this work we focus on substantial fractional integral and differential operators which play an important role in modeling anomalous diffusion. We introduce a new generalized substantial fractional integral. Generalizations of fractional…
Fractional differential and integral operators, Dirichlet averages, and splines of complex order are three seemingly distinct mathematical subject areas addressing different questions and employing different methodologies. It is the purpose…
We study fractional differential equations of Riemann-Liouville and Caputo type in Hilbert spaces. Using exponentially weighted spaces of functions defined on $\mathbb{R}$, we define fractional operators by means of a functional calculus…