Investigation of Exact Solutions of M-fractional Ivancevic Option Pricing Model Based on Three Different Methods

This paper is about the investigation of exact solutions of important economic model; Ivancevic option pricing model (IOPM) with M-fractional derivative. To achieve this aim, three different methods; expa function method, extended Sinh-Gordon equation expansion method (EShGEEM) and extended (G′/G)-expansion method are used. Obtained solutions consisting of trigonometric, hyperbolic trigonometric, rational and exponential. The obtained solutions are new than the existing solutions in the literature. The got solutions are also verified by using Mathematica tool. Graphically justification are also done by plotting 2-D,3-D and contour graphs. The importance of this paper is that M-fractional derivative is first time use for this model. On the bases of achieved results it is suggested that these methods are simple, reliable and fruitful than the other methods.