Abstract
In our research, we ascertain abundant novel exact traveling wave solutions of (2 + 1)-dimensional first integro-differential Kadomtsev-Petviashivili hierarchy equation by two new modified mathematical methods namely called generalized direct algebraic and extended simple equation methods with the help of computer package like Mathematica. These exact solutions are expressed in the forms of trigonometric, hyperbolic and rational function solutions which are established by using our eminent methods and also comparing our results to all of the well-known results that are given in the literature. These methods are more easier and having fruitful applications to solve different nonlinear wave problems in nonlinear science.