Introduction to fractional Orlicz-Sobolev spaces

2018/07/31 by Elhoussine Azroul, Azroul, Elhoussine, Abdelmoujib Benkirane +3
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.1807.11753

openalex publication_date 2018/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 and uniqueness of a solution for a non local problem involving the fractional M-Laplacian operator.

Related

• Basic results of fractional Orlicz-Sobolev space and applications to non-local problems
• Embedding theorems in the fractional Orlicz-Sobolev space and\n applications to non-local problems
• Compact embedding theorems and a Lions' type Lemma for fractional\n Orlicz-Sobolev spaces
• Ground state solutions for a non-local type problem in fractional Orlicz Sobolev spaces
• Boundedness of functions in fractional Orlicz-Sobolev spaces