ABSTRACT
This chapter describes a novel analytical method for getting the new exact solutions for fractional coupled non-linear equations like the time-fractional Korteweg–de Vries (KdV) –Burgers equation, time-fractional KdV-modified (mKdV) equation, time-fractional coupled Schrodinger–KdV equations, and time-fractional coupled Schrodinger–Boussinesq equations in plasma physics. The KdV–mKdV equation mainly describes the propagation of bounded particle of the atmosphere dust-acoustic solitary waves, internal solitary waves in shallow seas, and ion acoustic waves in plasmas with negative ions. The fractional differential equations can be described best in discontinuous media and the fractional order is equivalent to their fractional dimensions. The Burger equation is the special case of the KdV–Burgers equation which has been found to describe many types of physical phenomenon like turbulence and approximate theory of flow through a shock wave traveling in viscous fluid. The coupled Schrodinger–Boussinesq equations are originated from non-linear magnetosonic and upper-hybrid waves in magnetized plasma.
