Theory and Applications of Special Functions for Scientists and Engineers

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.

Addresses a family of the new special functions and provides the integral representations Gives the generalized integral transforms via Dunkl theory Presents the integral transforms via Kohlrausch-Williams-Watts function

Auteur
Xiao-Jun Yang PhD, is a professor of Applied Mathematics and Mechanics at China University of Mining and Technology, Xuzhou, China. His scientific interests include Mathematical Physics, Fractional Calculus and Applications, Fractals, Mechanics, Analytic Number Theory, Integral Transforms, and Special Functions. He recieved the Atanasije Stojkovic Medal, Belgrade, Serbia (2021). He was awarded the Abel Award (Istanbul, Turkey, 2020) for the achievements in the area of Fractional Calculus and its Applications. He was also awarded the Obada-Prize, Cairo, Egypt (2019). He was a recipient of the Young Scientist Award (2019) for the contributions in developing the Local Fractional Calculus at ICCMAS-2019, Istanbul, Turkey, and the Springer Distinguished Researcher Award (2019) at ICMMAAC-2019, Jaipur, India. He is the Highly Cited Researcher (2021,2020 and 2019, Clarivate Analytics) in Mathematics, and Elsevier Most Cited Chinese Researcher in Mathematics (2017, 2018, 2019, and 2020). He is one of the Scientific Committee of 10th edition of the Pan African Congress of Mathematicians. He is the author and co-author of 7 monographs for Elsevier, Springer Nature, CRC, World Science and Asian Academic, and co-editor of one edited book in De Gruyter.

Contenu

Chapter 1 Preliminaries.- Chapter 2 Wright Function and Integral Transforms via Dunkl Transform.- Chapter 3 Mittag-Leffler, Supertrigonometric and Superhyperbolic Functions.- Chapter 4 Wiman, Supertrigonometric and Superhyperbolic Functions.- Chapter 5 Prabhakar, Supertrigonometric and Superhyperbolic Functions.- Chapter 6 Other Special Functions Related to Mittag-Leffler Function.- Chapter 7 Kohlrausch-Williams-Watts Function and Related Topics Bibliography.