Stokes phenomenon for the M-Wright function of order 1n

Abstract

In this paper, using the higher-order differential equation of M-Wright function (Mainardi function) of order $\frac{1}{n},n\ge 3$, we get the integral representations for this function and other linear independent functions on the Laplace contours. The Stokes phenomenon and the Stokes/anti-Stokes rays for different domains in the complex plane are also investigated. Our approach is based on the steepest descent method for analyzing and drawing the steepest descent curves/directions for the initial values of n.