دانلود کتاب Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some ... in Science and Engineering, Volume 198)

This book is a landmark title in the continuous move from integer to non-integer in mathematics: from integer numbers to real numbers, from factorials to the gamma function, from integer-order models to models of an arbitrary order. For historical reasons, the word 'fractional' is used instead of the word 'arbitrary'.This book is written for readers who are new to the fields of fractional derivatives and fractional-order mathematical models, and feel that they need them for developing more adequate mathematical models.In this book, not only applied scientists, but also pure mathematicians will find fresh motivation for developing new methods and approaches in their fields of research.A reader will find in this book everything necessary for the initial study and immediate application of fractional derivatives fractional differential equations, including several necessary special functions, basic theory of fractional differentiation, uniqueness and existence theorems, analytical numerical methods of solution of fractional differential equations, and many inspiring examples of applications.A unique survey of many applications of fractional calculusPresents basic theoryIncludes a unified presentation of selected classical results, which are important for applicationsProvides many examplesContains a separate chapter of fractional order control systems, which opens new perspectives in control theoryThe first systematic consideration of Caputo's fractional derivative in comparison with other selected approachesIncludes tables of fractional derivatives, which can be used for evaluation of all considered types of fractional derivatives