In this article, several kinds of wave solutions such as solitons, solitary waves and Jacobi elliptic function solutions in which many are novel of nonlinear fractional partial differential equations (NLFPDEs) in mathematical physics, has obtained with the aid of improved extended auxiliary equation method. The efficiency of the current technique is demonstrated by applications to three NLFPDEs, namely,(2+ 1)-dimensional space-time fractional Zoomeron equation, space-time fractional Benjamin–Bona–Mahony and space-time fractional modified third-order KdV equations. Several kinds of exact solutions are constructed which have key applications in applied sciences. The geometrical shapes for some of the obtained results are depicted for various choices of the free parameters that appear in the results. The resulting numerous solutions will also be helpful in applied mechanics and various fields of sciences. This powerful technique can be applied to other wave models that can arise in mathematical physics.