Mittag-Leffler, Supertrigonometric, and Superhyperbolic Functions

Xiao-Jun Yang ()
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Xiao-Jun Yang: China University of Mining and Technology, School of Mathematics and State Key Laboratory for Geomechanics and Deep Underground Engineering

Chapter Chapter 3 in Theory and Applications of Special Functions for Scientists and Engineers, 2021, pp 255-366 from Springer

Abstract: Abstract In this chapter, we introduce the theory of the Mittag-Leffler function, supertrigonometric functions, and superhyperbolic functions. The integral representations for the Mittag-Leffler function and related functions are addressed and the general fractional calculus operators are also discussed in detail. The integral equations in the kernels of the Mittag-Leffler function, supertrigonometric functions, and superhyperbolic functions are presented; the truncated Mittag-Leffler, supertrigonometric, and superhyperbolic functions are considered; and some mathematical models are derived to explain the power-law behaviors in material science.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-33-6334-2_3

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DOI: 10.1007/978-981-33-6334-2_3

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