The fractional differential equation is a new research area of analytical mathematics, which provides useful tools to model many problems arising from mathematical physics, fluid dynamics, chemistry, biology, economics, control theory and image processing with memory effects. Function space theory has played an important role in the study of various fractional differential equations and complex real-world problems. Therefore, by using function space theory, understanding the characteristics of solutions and developing the properties of approximate solutions of this type of equations would have a profound impact on many disciplines. The new advancements of function space theory will greatly promote the development of fractional calculus theory, functional theory, and mathematical physics, as well as their applications in differential and integral equations.

This Special Issue aims to report and promote the latest achievements and recent developments in the well-posedness analysis and computational methods and function space theory for solving various fractional differential equations, also including by using fractional neural network technique to construct and train neural networks and deep learning neural networks to achieve better learning effect for artificial intelligence.

We invite researchers to submit original research articles as well as review articles on the recent development in the theory of function spaces and the applications of nonlinear fractional differential equations in sciences, technologies and engineering.

Potential topics include but are not limited to the following:

• Function space theory including fractional derivative
• Initial and boundary value problems of fractional differential equations
• Inequalities of fractional integrals and fractional derivatives
• Singular and impulsive fractional differential and integral equations
• Analysis and control in fractional differential equations including fractional network
• Numerical analysis and algorithm for fractional differential equations
• Fixed point theory and application in fractional calculus
• Fractional functional equations in function spaces
• Fractional methods for neural networks
• Fractional network arising in physical models
• Fractional stochastic differential equations