This research is dedicated to obtain Lie symmetries reduction, conservation newlinelaws, exact and approximate solution of some equations or system of nonlinear newlinefractional order partial differential equations (PDEs) which signify certain physical newlinephenomena. In this research the systems of the following forms are studied: newline Two dimensional time fractional PDEs with constant coefficients. newline Two dimensional space-time fractional PDEs with constant coefficients. newline Two dimensional space- time fractional PDEs with time dependent variable newlinecoefficients. newline Three dimensional fractional PDEs with constant coefficients. newline Four dimensional fractional PDEs with constant coefficients. newlineThis thesis consists of seven chapters. newlineChapter 1 is an introductory chapter which consists literature review, basic definitions, newlinemethodology and necessary preliminary related to the theory of symmetry newlineanalysis, conservation laws and some kind of solutions of fractional differential newlineequations. newlineiv newlineChapter 2 is devoted to the Lie group analysis of some space-time FPDEs newlinestructures with time-dependent variable coefficients involving the Riemann-Liouville newlinefractional derivative named as: the coupled Burgers system, the Ito system, the newlinecoupled Korteweg-de-Vries (KdV) equations, the Hirota-Satsuma coupled KdV equations newline(HSCKdV), the coupled nonlinear Hirota equations, which are successfully newlinereduced into system of fractional ordinary differential equations (FODEs) involving newlineErd` elyi-Kober fractional differential operators. newlineChapter 3 is concerned with the study of time-fractional Biswas Milovic equation. newlineThe considered equation has been reduced into a system of FODEs by Lie newlinesymmetry method. The soliton solutions for the equation by using the Da newlinet G newlineG expansion newlineapproach. The conservation law has been constructed. The numerical approximated newlinesolution has been obtained by the use of residual power series method newline(RPSM). newlineChapter 4 deals with analysis of space-time fractional variant Boussinesq system newlinewith constant coefficients.