Manuscript Topics

Nonlocal operators play an important role in both pure and applied mathematics. One of the most famous classes of such operators are the fractional differential and integral operators. These operators find applications in such diverse fields of mathematics as biological modeling, boundary value problems, and regularity theory for both elliptic PDEs and integral functionals, to name just a few areas. Nonlocal operators appear, more generally, in convolutions, which include the fractional differential and integral operators as special cases. Due to their inherently nonlocal structure, the mathematical analysis of these types of operators can be very challenging and fraught with difficulties and surprises. And there remain many open and interesting questions in this area of mathematics.

This special issue welcomes papers that in some way use or are related to nonlocal operators and their applications. Welcome topics include but are not limited to the following.

• Continuous or discrete fractional initial value problems
• Continuous or discrete fractional boundary value problems
• Nonlocal differential or difference equations (e.g., Kirchhoff-type differential equations)
• Properties or applications of compositions of nonlocal operators (e.g., sequential fractional equations)
• Applications of either the continuous or discrete fractional calculus
• Regularity theory for PDEs and integral functionals involving fractional derivatives and integrals in some manner
• Nonlocal models
• Qualitative properties of nonlocal operators (e.g., whether a nonlocal operator can detect when a function is monotone or convex)
• Problems involving convolution-type operators

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