Manuscript Topics

Nonlocal problems have a long history with significant theoretical and numerical developments in the last decades and successful applications in various fields. Compared with the local models, e.g. the classical integer-order partial differential equations, the nonlocal models provide adequate descriptions for complex phenomena such as the memory effects and nonlocal interactions. However, due to the nonlocality of these models, there are several difficulties that are not encountered in the studies of local models and remain to be investigated. With the rapid development of mathematical techniques and computational methods as well as the experimental evidences, there present growing motivations for the practical applications and mathematical investigations of the nonlocal models, which in turn inspire the organization of this special issue.

This special issue aims at promoting the investigations for different kinds of nonlocal problems from all aspects, such as modeling, theoretical analysis, numerical approximation and applications. We invite you to submit comprehensive review papers and original articles. This is an excellent opportunity for researchers to report their recent progresses with the scientific community, in general and particularly working in the fields related to the topics of the special issue, which include, but are not limited to, the following items:

• Fractional ordinary differential equations;  
• Time and/or space fractional partial differential equations;  
• Integral and integro-differential equations;  
• Peridynamics and fractional Laplacian;  
• Mathematical analysis;  
• Numerical analysis and scientific computing;  
• Optimal control and calculus of variations;  
• Inverse problems and ill-posed problems.

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