Department of Mathematics;
Faculty of Science and Art;
Pamukkale University;
Denizli 20160;
Türkiye;
Department of Physic;
Faculty of Science and Art;
Mustafa Kemal University;
Hatay 31001;
Türkiye;
Department of Mathematics;
Faculty of Science and Art;
Mustafa Kemal University;
Hatay 31001;
Türkiye;
conformable fractional derivative; new extended direct algebraic method; interacting wave equation; shallow water waves;