Related papers: Fractional Differentiation Operator over an Infini…
The transformation property of the Caputo fractional derivative operator of a scalar function under rotation in two dimensional space is derived. The study of the transformation property is essential for the formulation of fractional…
We define fractal interpolation on unbounded domains for a certain class of topological spaces and construct local fractal functions. In addition, we derive some properties of these local fractal functions, consider their tensor products,…
The Friedrichs extension for the generalized spiked harmonic oscillator given by the singular differential operator -D^2+ Bx^2 + Ax^{-2} + lambda x^{-alpha} (B>0, A >= 0) in L_2(0, infinity) is studied. We look at two different domains of…
After reviewing the problematic behavior of some previously suggested finite interval spatial operators of the symmetric Riesz type, we create a wish list leading toward a new spatial operator suitable to use in the space-time fractional…
Local solvability is analyzed for natural families of partial differential operators having double characteristics. In some families the set of all operators that are not locally solvable is shown to have both infinite dimension and…
In this article, we introduce the fractional maximal operator on the Hyperbolic space, a non-doubling measure space, and study the weighted boundedness. Motivated in the weighted boundedness of Hardy-Littlewood maximal studied by Antezana…
Fractional difference sequence spaces have been studied in the literature recently. In this work, some identities or estimates for the operator norms and the Hausdorff measures of noncompactness of certain operators on some difference…
In this article, we establish some conditions for the boundedness of fractional integral operators on the vanishing generalized weighted Morrey spaces. We also investigate corresponding commutators generated by BMO functions.
The fractional integrals and fractional derivatives problem is tackled by using the operator approach. The definition domain E of operators is causal functions.Many properties of fractional integrals are given. Fractional derivatives…
We consider additive functionals as a time and space-dependent function of a diffusion corresponding to nonhomogeneous uniformly elliptic divergence form operator. We show that if the function belongs to natural domain of strong solutions…
The paper deals with a fractional derivative introduced by means of the Fourier transform. The explicit form of the kernel of general derivative operator acting on the functions analytic on a curve in complex plane is deduced and the…
In this paper we examine boundedness of fractional maximal operator. The main focus is on commutators and maximal commutators on generalized Orlicz spaces for fractional maximal functions and Riesz potentials. We prove their boundedness…
In this paper, we study four nonlocal diffusion operators, including the fractional Laplacian, spectral fractional Laplacian, regional fractional Laplacian, and peridynamic operator. These operators represent the infinitesimal generators of…
We introduce and analyze an explicit formulation of fractional powers of the Lam\'e-Navier system of partial differential operators. We show that this fractional Lam\'e-Navier operator is a nonlocal integro-differential operator that…
We study the approximation properties of pseudo-differential operators with small time-frequency dispersion, meaning that their spreading functions are supported in a small neighborhood of the origin. It is commonly assumed that for such…
Fractional, anomalous diffusion in space-periodic potentials is investigated. The analytical solution for the effective, fractional diffusion coefficient in an arbitrary periodic potential is obtained in closed form in terms of two…
We study the fractional Laplacian $(-\Delta)^{\sigma/2}$ on the $n$-dimensional torus $\mathbb{T}^n$, $n\geq1$. First, we present a general extension problem that describes \textit{any} fractional power $L^\gamma$, $\gamma>0$, where $L$ is…
Although the study of functional calculus has already established necessary and sufficient conditions for operators to be fractionalized, this paper aims to use our well-conceived notion of integer powers of operators to construct…
We propose a novel extension to symmetrized neural network operators by incorporating fractional and mixed activation functions. This study addresses the limitations of existing models in approximating higher-order smooth functions,…
A generalization of exterior calculus is considered by allowing the partial derivatives in the exterior derivative to assume fractional orders. That is, a fractional exterior derivative is defined. This is found to generate new vector…