In recent years, fractional problems have begun to be introduced into Sobolev and Orlicz space and gradually generated the fractional Sobolev and Orlicz theory. These theories have attracted extensive attention from many scholars worldwide. They have been widely used in the fields of mathematics, finance, physics, and chemistry.

Concepts include non-local types of operators and equations on Sobolev and Orlicz spaces, (variable-order) fractional Laplace operators (with variable exponents), fractional magnetic operators, fractional p(x)-Laplacian, and so on. It is our main goal to involve these various types of operators in partial differential equations. Many new theorems of continuous embedding and compact embedding about these operators in space need to be studied and perfected. At the same time, we also pay attention to the existence and multiplicity of solutions, as well as the asymptotic behaviour, monotonicity, symmetry, and regularity.

The aim of this Special Issue is to collect original and high-quality research and review articles related to the development of the theory and method of fractional equations with variable exponents and their applications. We welcome in-depth studies of existing problems and some problems that have never been solved. We encourage submissions relating to new embedding theorems and inequalities of Sobolev and Orlicz space and the related problems in the theory.

Potential topics include but are not limited to the following:

• Variational methods and their application
• Fractional differential problems with variable exponents
• Fractional Schrodinger equations with variable exponents
• Fractional magnetic operator equations with variable exponents
• Variable-order fractional problems
• Fractional Sobolev and Orlicz space and their applications
• Embedding theorems and inequalities of Sobolev and Orlicz space
• Critical point theorems and their applications
• Fractional Kirchhoff equations and their applications