Recent Advance in Function Spaces and Their Applications in Fractional Differential Equations

Xinguang Zhang, Lishan Liu, Yonghong Wu, Liguang Wang
2019 Journal of Function Spaces  
Fractional calculus is a new branch of analytical mathematics which provides useful tools to model many physical and biological phenomena and optimal control of complex processes with memory effects. Therefore, new advancement of fractional calculus theory will greatly promote the development of function space theory, functional theory, and mathematical physics as well as their applications in differential and integral equations. This special issue mainly focuses on the latest achievements and
more » ... ecent development of fractional calculus in the nonlinear analysis, optimal control, computational methods, space theory, and applications for solving various fractional differential equations; it contains 46 papers selected through a rigorous peer-reviewed process. These papers almost cover most of directions and applications in fractional calculus. In what follows, we briefly review the highlights and main contributions of each paper. In the paper titled "Existence Results for a Class of Semilinear Fractional Partial Differential Equations with Delay in Banach Spaces", the authors consider the existence and uniqueness of the mild solutions for a class of nonlinear time fractional partial differential equations with delay by using the theory of solution operator and the general Banach contraction mapping principle.
doi:10.1155/2019/5719808 fatcat:mwdi7rybjvabjot56zpesc6f7a