Advances in fractional differential equations (IV): Time-fractional PDEs

The fractional calculus (FC) started more than three centuries ago. In the last years, FC is playing a very important role in various scientific fields. In fact, FC has been recognized as one of the best tools to describe long-memory processes. Fractional-order models are interesting not only for engineers and physicists, but also for mathematicians. Among such models those described by partial differential equations (PDEs) containing fractional derivatives are of utmost importance. Their evolution was more complex than for the classical integer-order counterpart. Nonetheless, classical PDEs’ methods are hardly applicable directly to fractional PDEs. Therefore, new theories and methods are required, with concepts and algorithms specifically developed for fractional PDEs. This is the fourth special issue on Advances in Fractional Differential Equations of the journal Computers and Mathematics with Applications. This selection of 38 papers focuses on innovative theoretical and numerical methods, and in applications of FC to important problems that encompass the most relevant areas of current research on fractional PDEs.info:eu-repo/semantics/publishedVersio