Search

An Introduction to Hypergeometric, Supertigonometric, and Superhyperbolic Functions gives a basic introduction to the newly established hypergeometric, supertrigonometric, and superhyperbolic functions from the special functions viewpoint. The special functions, such as the Euler Gamma function, the Euler Beta function, the Clausen hypergeometric series, and the Gauss hypergeometric have been successfully applied to describe the real-world phenomena that involve complex behaviors arising in mathematics, physics, chemistry, and engineering. - Provides a historical overview for a family of the special polynomials - Presents a logical investigation of a family of the hypergeometric series - Proposes a new family of the hypergeometric supertrigonometric functions - Presents a new family of the hypergeometric superhyperbolic functions

This book provides the knowledge of the newly-established supertrigonometric and superhyperbolic functions with the special functions such as Mittag-Leffler, Wiman, Prabhakar, Miller-Ross, Rabotnov, Lorenzo-Hartley, Sonine, Wright and Kohlrausch-Williams-Watts functions, Gauss hypergeometric series and Clausen hypergeometric series. The special functions can be considered to represent a great many of the real-world phenomena in mathematical physics, engineering and other applied sciences. The audience benefits of new and original information and references in the areas of the special functions applied to model the complex problems with the power-law behaviors.The results are important and interesting for scientists and engineers to represent the complex phenomena arising in applied sciences therefore graduate students and researchers in mathematics, physics and engineering might find this book appealing.

General Fractional Derivatives with Applications in Viscoelasticity introduces the newly established fractional-order calculus operators involving singular and non-singular kernels with applications to fractional-order viscoelastic models from the calculus operator viewpoint. Fractional calculus and its applications have gained considerable popularity and importance because of their applicability to many seemingly diverse and widespread fields in science and engineering. Many operations in physics and engineering can be defined accurately by using fractional derivatives to model complex phenomena. Viscoelasticity is chief among them, as the general fractional calculus approach to viscoelasticity has evolved as an empirical method of describing the properties of viscoelastic materials. General Fractional Derivatives with Applications in Viscoelasticity makes a concise presentation of general fractional calculus. - Presents a comprehensive overview of the fractional derivatives and their applications in viscoelasticity - Provides help in handling the power-law functions - Introduces and explores the questions about general fractional derivatives and its applications

General Fractional Derivatives: Theory, Methods and Applications provides knowledge of the special functions with respect to another function, and the integro-differential operators where the integrals are of the convolution type and exist the singular, weakly singular and nonsingular kernels, which exhibit the fractional derivatives, fractional integrals, general fractional derivatives, and general fractional integrals of the constant and variable order without and with respect to another function due to the appearance of the power-law and complex herbivores to figure out the modern developments in theoretical and applied science. Features: Give some new results for fractional calculus of constant and variable orders. Discuss some new definitions for fractional calculus with respect to another function. Provide definitions for general fractional calculus of constant and variable orders. Report new results of general fractional calculus with respect to another function. Propose news special functions with respect to another function and their applications. Present new models for the anomalous relaxation and rheological behaviors. This book serves as a reference book and textbook for scientists and engineers in the fields of mathematics, physics, chemistry and engineering, senior undergraduate and graduate students. Dr. Xiao-Jun Yang is a full professor of Applied Mathematics and Mechanics, at China University of Mining and Technology, China. He is currently an editor of several scientific journals, such as Fractals, Applied Numerical Mathematics, Mathematical Modelling and Analysis, International Journal of Numerical Methods for Heat & Fluid Flow, and Thermal Science.

The book is devoted to recent developments in the theory of fractional calculus and its applications. Particular attention is paid to the applicability of this currently popular research field in various branches of pure and applied mathematics. In particular, the book focuses on the more recent results in mathematical physics, engineering applications, theoretical and applied physics as quantum mechanics, signal analysis, and in those relevant research fields where nonlinear dynamics occurs and several tools of nonlinear analysis are required. Dynamical processes and dynamical systems of fractional order attract researchers from many areas of sciences and technologies,ranging from mathematics and physics to computer science.

Local Fractional Integral Transforms and Their Applications provides information on how local fractional calculus has been successfully applied to describe the numerous widespread real-world phenomena in the fields of physical sciences and engineering sciences that involve non-differentiable behaviors. The methods of integral transforms via local fractional calculus have been used to solve various local fractional ordinary and local fractional partial differential equations and also to figure out the presence of the fractal phenomenon. The book presents the basics of the local fractional derivative operators and investigates some new results in the area of local integral transforms. - Provides applications of local fractional Fourier Series - Discusses definitions for local fractional Laplace transforms - Explains local fractional Laplace transforms coupled with analytical methods