Abstract
In this study, the (3+1)-dimensional fractional time-space Kadomtsev-Petviashivili (FTSKP) equation is considered and analyzed analytically, which propagates the acoustic waves in an unmagnetized dusty plasma. The fractional derivatives are studied in a confirmable sense. The new modified extended direct algebraic (MEDA) approach is adopted to investigate the diverse nonlinear wave structures. A variety of new families of hyperbolic and trigonometric solutions are obtained in single and different combinations. The obtained results are also constructed graphically with the different parametric choices.