This study is devoted to a class of linear and nonlinear differential equations with fractionalorder governing diffusion, Burger’s, Airy’s, KdV, gas dynamic and Fisher’s equations. These equations are used to describe the physical processes of models possessing memory. By employing classical and nonclassical Lie symmetry analysis and some technical calculations, new infinitesimal generators are obtained which give rise to derive the invariant solutions for this class of equations.
