In this article, we study the existence of integral solutions for two classes of fractional order evolution equations with nondensely defined linear operators. First, we consider the nonhomogeneous fractional order evolution equation and obtain its integral solution by Laplace transform and probability density function. Subsequently, based on the form of integral solution for nonhomogeneous fra...

This paper presents a numerical method for solving the Volterra integral equation with a convolution kernel. The integral equation was first converted to an algebraic equation using the Laplace transform, after which its numerical inversion was determined by power series. The Padé approximants were effectively used to improve the convergence rate and accuracy of the computed series. The method ...

We sketch the integral transform method in a close connection with its historical development and survey newer applications to problems in production economics and finance.