دانلود کتاب سیستم های دینامیکی کسری محاسباتی- معادلات دیفرانسیل کسری و کاربردها

Subject of fractional calculus has gained considerable popularity and importance during the past three decades, mainly due to its validated applications in various fields of science and engineering. It deals with the differential and integral operators with nonintegral powers. Fractional differential equations are the pillar of various systems occurring in a wide range of science and engineering applications, namely physics, chemical engineering, mathematical biology, financial mathematics, structural mechanics, control theory, circuit analysis, and biomechanics. The fractional derivative has also been used in various other physical problems, such as frequency-dependent damping behavior of structures, the motion of a plate in a Newtonian fluid, and PIλDμcontroller for the control of dynamical systems. The mathematical models in electromagnetics, rheology, viscoelasticity, electrochemistry, control theory, Brownian motion, signal and image processing, fluid dynamics, financial mathematics, and material science are well defined by fractional-order differential equations. Generally, these physical models are demonstrated either by ordinary or partial differential equations. But, modeling these problems by fractional differential equations sometimes makes the physics of the systems more practical. In order to know the behavior of these systems, we need to study the solutions of the governing fractional equations. The exact solution of fractional differential equations may not always be possible using known classical methods. Generally, the physical models occurring in nature comprise complex phenomena. So, it is challenging to get the solution (both analytical and numerical) of nonlinear differential equations of fractional order. For the last few decades, a great deal of attention has been directed toward the solution to these kinds of problems. Researchers throughout the globe are trying to develop various efficient methods to handle these problems. Although there exist a variety of standard books related to the solution of fractional differential equations and related methods. But, the existing books are method specific or subject specific or sometimes may not be efficient. Few existing books deal with basic numerical and analytical methods for solving the fractional differential equations, whereas some other books may be found related to particular semi-analytical methods only. But, as per the authors’ knowledge, books covering the basic concepts of the computationally efficient and variety of advanced methods in one place in a systematic manner are rare.