Application of the Efros Theorem to the Function Represented by the Inverse Laplace Transform of s−μ exp(−sν)

Symmetry

Alexander Apelblat¹  Francesco Mainardi² 

[1] Department of Chemical Engineering, Ben Gurion University of the Negev, Beer Sheva 84105, Israel;Dipartimento di Fisica e Astronomia, Università di Bologna, Via Irnerio 46, I-40126 Bologna, Italy;

关键词: efros theorem;    inverse laplace transforms;    wright functions;    Mittag–Leffler functions;    volterra functions;    modified bessel functions;   

DOI  :  10.3390/sym13020354

来源: DOAJ

【 摘 要 】

Using a special case of the Efros theorem which was derived by Wlodarski, and operational calculus, it was possible to derive many infinite integrals, finite integrals and integral identities for the function represented by the inverse Laplace transform. The integral identities are mainly in terms of convolution integrals with the Mittag–Leffler and Volterra functions. The integrands of determined integrals include elementary functions (power, exponential, logarithmic, trigonometric and hyperbolic functions) and the error functions, the Mittag–Leffler functions and the Volterra functions. Some properties of the inverse Laplace transform of $s^{-\mu }\exp (-s^{\nu })$ with $\mu \ge 0$ and $0<\nu <1$ are presented.

【 授权许可】

Unknown