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OverviewThis book aims to establish a foundation for fractional derivatives and fractional differential equations. The theory of fractional derivatives enables considering any positive order of differentiation. The history of research in this field is very long, with its origins dating back to Leibniz. Since then, many great mathematicians, such as Abel, have made contributions that cover not only theoretical aspects but also physical applications of fractional calculus. The fractional partial differential equations govern phenomena depending both on spatial and time variables and require more subtle treatments. Moreover, fractional partial differential equations are highly demanded model equations for solving real-world problems such as the anomalous diffusion in heterogeneous media. The studies of fractional partial differential equations have continued to expand explosively. However we observe that available mathematical theory for fractional partial differential equations is not still complete. In particular, operator-theoretical approaches are indispensable for some generalized categories of solutions such as weak solutions, but feasible operator-theoretic foundations for wide applications are not available in monographs. To make this monograph more readable, we are restricting it to a few fundamental types of time-fractional partial differential equations, forgoing many other important and exciting topics such as stability for nonlinear problems. However, we believe that this book works well as an introduction to mathematical research in such vast fields. Full Product DetailsAuthor: Adam Kubica , Katarzyna Ryszewska , Masahiro YamamotoPublisher: Springer Verlag, Singapore Imprint: Springer Verlag, Singapore Edition: 1st ed. 2020 Weight: 0.454kg ISBN: 9789811590658ISBN 10: 9811590656 Pages: 134 Publication Date: 30 November 2020 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand We will order this item for you from a manufactured on demand supplier. Table of ContentsReviewsThe book is written nicely and useful as an introductory book on time fractional derivatives in abstract spaces. (Syed Abbas, zbMATH 1485.34002, 2022) “The book is written nicely and useful as an introductory book on time fractional derivatives in abstract spaces.” (Syed Abbas, zbMATH 1485.34002, 2022) Author InformationTab Content 6Author Website:Countries AvailableAll regions |