An auxiliary equation technique is applied to investigate a generalized Benjamin-Bona-Mahony equation with variable coefficients. Many exact traveling wave solutions are obtained which include algebraic solutions, solitons, solitary wave solutions and trigonometric solutions. Mathematics Subject Classification: 35Q53, 35B35

In this research, three numerical methods, namely the variational iteration method, Adomian decomposition and homotopy analysis method are considered to achieve an approximate solution for a third-order time-fractional partial differential Equation (TFPDE). The equation is obtained from classical (FW) by replacing integer-order time derivative with Caputo fractional of order η=(0,1] variable co...