Mehmet Senol - Nevsehir Haci Bektas Veli University, Department of Mathematics, Nevsehir, Turkey
Emad Az-Zobi - Mutah University, Department of Mathematics and Statistics, Al-Karak, Jordan
Lanre Akinyemi - Prairie View A&M University, Department of Mathematics, Prairie View, TX, USA
Ahmed Alleddawi - Mutah University, Department of Mathematics and Statistics, Al-Karak, Jordan

In this study, our main goal is to study the exact traveling wave solutions of some recent nonlinear evolution equations, namely, modified generalized (۳+۱)-dimensional time-fractional Kadomtsev–Petviashvili (KP) and Kadomtsev-Petviashvili-Benjamin-Bona-Mahony (KP-BBM) equations of conformable type. We employed a consistent analytical method called the generalized Riccati equation mapping method, along with a conformable derivative to extract the multiple kinks, bi-symmetry soliton, bright and dark soliton solutions, periodic solutions, and singular solutions for suggested equations. The theoretical method is based on the Riccati equation and a number of empirical solutions have been proposed that do not exist in the literature. Furthermore, as the order of the fractional derivative approaches one, the exact solutions obtained by the current method are reduced to classical solutions. The obtained results show that the present technique is effective, easy to implement, and a strong tool for solving nonlinear fractional partial differential equations, and produces a very large number of solutions.

Conformable derivative, Generalized KP-BBM equation, Generalized Riccati equation mapping method, Generalized KP equation, Soliton solutions