Application of the Exp-Function and Generalized Kudryashov Methods for Obtaining New Exact Solutions of Certain Nonlinear Conformable Time Partial Integro-Differential Equations

The key objective of this paper is to construct exact traveling wave solutions the conformable time second integro-differential Kadomtsev–Petviashvili (KP) hierarchy equation using Exp-function method and (2 + 1)-dimensional partial Jaulent–Miodek (JM) evolution utilizing generalized Kudryashov method. These two problems involve derivative with respect time. Initially, equations can be converted into nonlinear ordinary differential via a fractional complex transformation. resulting are then analytically solved corresponding methods. As result, explicit for these expressed in terms exponential functions. Setting some specific parameter values varying order equations, their 3D, 2D, contour graphically shown physically characterized as, instance, bell-shaped solitary solution, kink-type singular multiple-soliton solution. To best authors’ knowledge, results obtained proposed methods novel reported here first simple, very powerful, reliable solving other arising many applications.