Some features and applications of the Mittag-Leffler function

This thesis is concerned with the Mittag-Leffler (M-L) function and some of its analytical properties and applications, and consists of five chapters. In Section 1, an introduction to the Mittag-Leffler function is given and then the uses of this function in many scientific disciplines will be explained. In Section 2, some fundamental definitions and theorems are given to be used in the next two sections of the thesis. In Section 3, the explicit formulas of the Mittag-Leffler function with one and two variables are given and their Laplace transforms are calculated. In Section 4, some relations between Mittag-Leffler with one parameter and two parameters are given. The main result of this section is to give the recurrence relations for Mittag-Leffler function with one variable and two variables. In Section 5, some conclusions and recommendations are made