In this research project, an implicit meshless method has been presented to solve 2D fractional stochastic Tricomi-type equation on irregular domains. This scheme is combination of finite difference method and meshless method based on radial basis function. This research project embraces four chapters which are presented as follows. Meshless method based on radial basis functions to approximate functions, different kinds of radial basis functions, necessary definitions and theorems are given in chapter 1. Initial definitions and preliminaries of fractional calculus are developed in chapter 2. Chapter 3 is an overview of introductions and initial definitions of probability theory and stochastic processes. Then, Brownian motion which is one of the most important stochastic processes and plays a significant role in stochastic differential equations and stochastic integral equations is introduced. Chapter 4 devoted to numerical solution of 2D fractional stochastic Tricomi-type Equation by using an implicit meshless method. At the end of this chapter, some numerical examples are included to illustrate accuracy, efficiency and applicability of the mentioned approach.
