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Using a special case of the Efros theorem which was derived by Wlodarski, andoperational calculus, it was possible to derive many infinite integrals, finiteintegrals and integral identities for the function represented by the inverseLaplace transform. The integral identities are mainly in terms of convolutionintegrals with the Mittag-Leffler and Volterra functions. The integrands ofdetermined 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 theinverse Laplace transform of $s^{-\mu} \exp(-s^\nu)$ with $\mu \ge0$ and$0<\nu<1$ are presented

Application of the Efros theorem to the function represented by the inverse Laplace transform of $s^{-\mu}\,\exp(-s^\nu)$