Abstarct: The main purpose of the present thesis is a comprehensive and general analysis of the application of Lie groups in fractional differential equation including their solving method and conservation laws.‎ ‎ The extended dynamical systems with movement and motion's memory don't follow from the ordinary derivatives rules. Because of the more exactness of the models for engineering systems than integer orders fractional derivatives and integrals and more interesting for researchers.‎ ‎ Obtaining solutions for a system of fractional differential equations has great importance, thus choosing the suitable methods with respect to fractional structures is so valuable. In this thesis, the Lie symmetry method is studied baxsed on the extension of the symmetry ‎of ‎the ‎equation‎s with integer order derivatives. Also, some analytic method such as invariant subspace and sub-equation are studied and comparison too.‎ ‎ Finally, for the importance of the differential equations in financial mathematics, the symmetry method for fractional differential equations as a geometric method, are applied in order to study some equation in financial mathematics such as Fokker-Plank and etc.