The class of almost periodic functions was first introduced by Danish mathematician Harald Bohr around 1925, and later generalised by many other mathematicians. The most important generalisations of the Bohr almost periodic functions are Stepanov almost periodic functions, Weyl almost periodic functions, and Besicovitch almost periodic functions. Any (Bohr) almost periodic function is continuous, which is no longer true in the concepts developed by H. Weyl and A. S. Besicovitch.

There is an enormous literature devoted to the study of almost periodic solutions of abstract (degenerate, functional) Volterra integro-differential equations and abstract (degenerate) fractional integro-differential equations in Banach spaces and locally convex spaces. However, it is very difficult and unpleasant to say precisely who was the first to study the almost periodic solutions of abstract fractional (functional) differential equations.

The main aim of this Special Issue is to present the latest theoretical ideas and methodological developments in the theory of almost periodic functions and their applications to abstract Volterra integro-differential equations in Banach spaces and locally convex spaces, degenerate or non-degenerate in the time variable. Covered topics also include recent developments in the theory of almost automorphic functions, introduced by the American mathematician S. Bochner in 1962, and their applications to abstract Volterra integro-differential equations. Applications to semilinear abstract Volterra integro-differential equations are also welcomed, including the recent developments in fixed point theory. We welcome both original research and review articles.

Potential topics include but are not limited to the following:

• Almost periodic functions
• Almost automorphic functions
• Abstract degenerate Volterra integro-differential equations
• Abstract non-degenerate Volterra integro-differential equations
• Abstract degenerate fractional integro-differential equation
• Abstract non-degenerate fractional integro-differential equations
• Fixed point theory
• Semilinear abstract degenerate Volterra integro-differential equations
• Semilinear abstract non-degenerate Volterra integro-differential equations
• Semilinear abstract degenerate fractional integro-differential equations
• Semilinear abstract non-degenerate fractional integro-differential equations
• Abstract (semilinear) functional degenerate Volterra integro-differential equations
• Abstract (semilinear) functional non-degenerate Volterra integro-differential equations
• Abstract (semilinear) functional fractional Volterra integro-differential equations
• Abstract (semilinear) functional degenerate Volterra integro-differential equations
• Uniformly recurrent functions and their applications