Introduction to Analysis

Analysis is the systematic study of real and complex-valued continuous functions. Important subfields of analysis include calculus, differential equations, and functional analysis. Various special functions like Bessel and all cylindrical functions; the Gauss, Kummer, confluent and generalized hypergeometric functions; the classical orthogonal polynomials, the incomplete Gamma and Beta functions and error functions, and so on, will provide solutions to integer order differential equations and systems, used as mathematical models. Real analysis and complex analysis are two broad subdivisions of analysis which deal with real-values and complex-valued functions, respectively. However, recently there has been an increasing interest in and widely extended use of differential equations and systems of fractional order (that is, of arbitrary order), as better models of phenomena of various physics, engineering, automatization, biology and biomedicine, chemistry, earth science, economics, nature and so on. This book presents state of the art in mathematical analysis and its numerous applications. It provides students, practitioners, and researchers with the opportunity to develop an understanding of special functions and the skills needed to apply advanced mathematical techniques to solve complex engineering problems. It is intended to highlight the importance of fundamental results and techniques of the theory of mathematical analysis, and emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions.