Asymptotic Laplace Transforms and Evolution Equations

Vector-valued Laplace Transforms and Cauchy Problems

This monograph gives a systematic account of the theory of vector-valued Laplace transforms, ranging from representation theory to Tauberian theorems. In parallel, the theory of linear Cauchy problems and semigroups of operators is developed completely in the spirit of Laplace transforms. Existence and uniqueness, regularity, approximation and above all asymptotic behaviour of solutions are stu...

Autoconvolution equations and generalized Mittag-Leffler ‎functions

This article is devoted to study of the autoconvolution equations and generalized Mittag-Leffler functions. These types of equations are given in terms of the Laplace transform convolution of a function with itself. We state new classes of the autoconvolution equations of the first kind and show that the generalized Mittag-Leffler functions are solutions of these types of equations. In view of ...

A note on the comparison between Laplace and Sumudu transforms

L2-transforms for boundary value problems

In this article, we will show the complex inversion formula for the inversion of the L2-transform and also some applications of the L2, and Post Widder transforms for solving singular integral equation with trigonometric kernel. Finally, we obtained analytic solution for a partial differential equation with non-constant coefficients.

Infinite-series Representations of Laplace Transforms of Probability Density Functions for Numerical Inversion

In order to numerically invert Laplace transforms to calculate probability density functions (pdf’s) and cumulative distribution functions (cdf’s) in queueing and related models, we need to be able to calculate the Laplace transform values. In many cases the desired Laplace transform values (e.g., of a waiting-time cdf) can be computed when the Laplace transform values of component pdf’s (e.g.,...