ABSTRACT
In recent years, the study of fractional ordinary differential equations (FODEs) and fractional partial differential equations (FPDEs) has attracted much attention due to an exact description of nonlinear phenomena in fluid mechanics, viscoelasticity, biology, physics, engineering and other areas of science. In reality, a physical phenomenon may depend not only on the time instant but also on the previous time history, which can be successfully modeled by using the theory of derivatives and integrals of fractional order. The time and space FPDEs are obtained by replacing the integer order time and space derivatives in PDEs by the fractional derivative of order α > 0. In this chapter, different FODEs and FPDEs are investigated by the Lie symmetry method and invariant subspace method.
