Editorial

Abstract

In the past forty years, fractional calculus had played a very important role in various fields such as mechanics, electricity, chemistry, biology, economics, control theory, and signal and image processing [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15].In the last decade, fractional calculus has been recognised as one of the best tools to describe long-memory processes. Such models are interesting for engineers and physicists but also for pure mathematicians. The most important among such models are those described by partial differential equations (PDEs) containing fractional derivatives. Their evolutions behave in a much more complex way than in the classical integer-order case and the study of the corresponding dynamics is a hugely demanding task. Although some results of qualitative analysis for fractional partial differential equations (FPDEs) can be similarly obtained, many classical PDEs' methods are hardly applicable directly to FPDEs. New theories and methods are thus required to be specifically developed for FPDEs, whose investigation becomes more challenging. Comparing with PDEs' classical theory, the research on FPDEs is only at an initial stage of development.This special issue on Dynamics of Fractional Partial Differential Equations consists of 20 original articles covering various aspects of FPDEs and their applications. These papers could be grouped into four categories, namely, survey of fractional calculus [22], numerical methods to solve FPDEs [17,23,[26][27][28][32][33][34], qualitative analysis of FPDEs [16,18,21,24,30,35] and application of FPDEs in various fields [19,20,25,29,31].In paper [16] the theory of Hausdorff measure of noncompactness and fixed point theorems are applied to study the abstract nonlocal Cauchy problem of a class a

Introduction to colloidal dispersions in external fields

“…Accordingly, a collective ensemble of charged colloids responds in an even more complicated way to an external electric field. In this special issue, electrokinetics will be accessed by experimental studies [26,27] by computer simulations [28,29] and by statistical theory [30].…”