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 ...

We present a numerical approximate solution to Sobolev-type differential equation subject to nonlocal initial boundary conditions. A Laplace transform method is described for the solution of considered equation. Following Laplace transform of the original problem, an appropriate method of solving differential equations is used to solve the resultant time-independent modified equation and soluti...