In this paper, we apply two different methods, namely, the G G-expansion method and G G 2-expansion method to investigate the nonlinear time fractional Harry Dym equation in the Caputo sense and the symmetric regularized long wave equation in the conformable sense. The mentioned NPDES arise in diverse physical applications like ion sound waves in plasma and waves on shallow water surfaces. There exist multiple wave solutions to many NPDEs and one is interested in analytical approaches for obtaining multiple wave solutions to NPDEs. The multi-exp-function method formulates a solution algorithm for calculating multiple wave solutions to NPDEs and at the end of paper, we apply the MEFM for calculating multiple wave solutions to the (2+1)-dimensional equation.