Related papers: Basic results of fractional Orlicz-Sobolev space a…

In this paper, we define the fractional Orlicz-Sobolev spaces, and we prove some important results of these spaces. The main result is to show the continuous and compact embedding for these spaces. As an application, we prove the existence…

In this paper, we investigate the existence of weak solution for a fractional type problems driven by a nonlocal operator of elliptic type in a fractional Orlicz-Sobolev space, with homogeneous Dirichlet boundary conditions. We first extend…

In this work, we establish some abstract results on the perspective of the fractional Musielak-Sobolev spaces, such as: uniform convexity, Radon-Riesz property with respect to the modular function, $(S_{+})$-property, Brezis-Lieb type Lemma…

For the nonlocal quasilinear fractional $p$-Laplace operator $(-\Delta)^s_p$ with $s\in (0,1)$ and $p\in(1,\infty)$, we investigate the nonexistence and existence of nontrivial nonnegative solutions $u$ in the local fractional Sobolev space…

In this paper we prove compact embedding of a subspace of the fractional Orlicz-Sobolev space $W^{s, G}\left(\mathbb{R}^{N}\right)$ consisting of radial functions, our target embedding spaces are of Orlicz type. Also, we prove a Lions and…

In this paper, we study the following nonlocal problem in fractional Orlicz Sobolev spaces \begin{eqnarray*} (-\Delta_{\Phi})^{s}u+V(x)a(|u|)u=f(x,u),\quad x\in\mathbb{R}^N, \end{eqnarray*} where $(-\Delta_{\Phi})^{s}(s\in(0, 1))$ denotes…

In the present paper, we deal with a new continuous and compact embedding theorems for the fractional Orlicz-Sobolev spaces, also, we study the existence of infinitely many nontrivial solutions for a class of non-local fractional…

Graph-based analysis holds both theoretical and applied significance, attracting considerable attention from researchers and yielding abundant results in recent years. However, research on fractional problems remains limited, with most of…

The study of certain differential operators between Sobolev spaces of sections of vector bundles on compact manifolds equipped with rough metric is closely related to the study of locally Sobolev functions on domains in the Euclidean space.…

In this paper, we introduce and study a new class of fractional modular function spaces, called \emph{Fractional Anisotropic Musielak--Sobolev Spaces}, which generalize both the fractional Anisotropic Orlicz--Sobolev spaces and the…

In this paper, we develop some properties of the $a_{x,y}(.)$-Neumann derivative for the fractional $a_{x,y}(.)$-Laplacian operator. Therefore we prove the basic proprieties of the correspondent function spaces. In the second part of this…

In this paper, we investigate the existence of weak solution for a Kirchhoff type problem driven by a nonlocal operator of elliptic type in a fractional Orlicz-Sobolev space, with homogeneous Dirichlet boundary conditions {\small$$…

In this paper, we first define a discrete version of the fractional Laplace operator $(-\Delta)^{s}$ through the heat semigroup on a stochastically complete, connected, locally finite graph $G = (V, E, \mu, w)$. Secondly, we define the…

Fractional operators are widely used in mathematical models describing abnormal and nonlocal phenomena. Although there are extensive numerical methods for solving the corresponding model problems, theoretical analysis such as the regularity…

We study integral operators $\mathcal{L}u(x)=\int_{\mathbb{R^N}}\psi(u(x)-u(y))J(x-y)\,dy$ of the type of the fractional $p$-Laplacian operator, and the properties of the corresponding Orlicz and Sobolev-Orlicz spaces. In particular we show…

The main goal of this paper is to introduce a new fractional anisotropic Sobolev space with variable exponent where the basic qualitative properties (completeness, separability, reflexivity, ...) are established, including the continuous…

The objective of this paper is twofold. First, we conduct a careful study of various functional inequalities involving the fractional Laplacian operators, including nonlocal Sobolev-Poincar\'e, Nash, Super Poincar\'e and logarithmic Sobolev…

Let $G$ be an Orlicz function and let $ \alpha, \beta, s$ be positive real numbers. Under certain conditions on the Orlicz function $ G $, we establish some continuous embeddings results between the fractional order Orlicz-Sobolev spaces…

We consider the one and the two obstacles problems for the nonlocal nonlinear anisotropic $g$-Laplacian $\mathcal{L}_g^s$, with $0<s<1$. We prove the strict T-monotonicity of $\mathcal{L}_g^s$ and we obtain the Lewy-Stampacchia…

In this paper, we study the existence of positive non-decreasing radial solutions of a nonlocal non-standard growth problem ruled by the fractional $g$-Laplace operator with exterior Neumann condition. Our argument exploits some properties…