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In this research paper, we implement the sine-Gordon expansion method to two governing models which are the (2+1)-dimensional Nizhnik–Novikov–Veselov equation and the Caudrey–Dodd–Gibbon–Sawada–Kotera equation. We use conformable derivative to transform these nonlinear partial differential models to ordinary differential equations. We find some wave solutions having trigonometric function, hyperbolic function. Under the strain conditions of these solutions obtained in this paper, various simulations are plotted. [ABSTRACT FROM AUTHOR]

This paper constructs approximate solutions of the epidemic system of HIV/AIDS transmission model with the help of the conformable fractional differential transform method. The fractional derivatives considered in this paper are described in the sense of the conformable operator. This method provides the approximate solutions speedily in the form of a convergent series. The results show the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

This paper constructs dark, bright, combined dark-bright, singular, combined singular soliton optical and singular periodic solutions to the conformable space-time fractional second order nonlinear Schrödinger equation with group velocity dispersion coefficient and spatiotemporal dispersion by using the extended sinh-Gordon equation expansion method. The constraint conditions for the existence of valid soliton solutions are given. The reported results in this study may be helpful in explaining the physical meaning of the studied model. [ABSTRACT FROM AUTHOR]

• Conformable 3D Wazwaz-Benjamin-Bona-Mahony (3D-WBBM) equation is studied. • A variety of nonlinear dynamical solitary wave structures are extracted. • Bell shaped, shock, singular and multiple soliton are reported. • Generalized exponential rational function method (GERFM) is considered. • The physical characterization of results graphically in 3D, 2D are figured out. In this article, we elucidate the dynamical behavior of exact solitary waves to the conformable 3D Wazwaz-Benjamin- Bona-Mahony (3D-WBBM) equation emerging in shallow water waves. A variety of nonlinear dynamical solitary wave structures are extracted in different shapes like hyperbolic, trigonometric, and exponential function solutions including some special known solitary wave solution like bell shaped, shock, singular and multiple soliton by an analytical mathematical tool namely the generalized exponential rational function method (GERFM). Besides, we also secure singular periodic wave solutions with unknown parameters. All the secured solutions are verified by substituting back to the original equation through soft computation Mathematica. The outcomes show that the governing model theoretically possesses extremely rich structures of exact solitary wave solutions. The physical characterization of some reported results are figured out graphically in 3D, 2D and their corresponding contour profiles by selecting appropriate values of parameters. [ABSTRACT FROM AUTHOR]