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In this paper, a local fractional Riccati differential equation method is applied. A new travelling wave solution to the nonlinear local fractional (2 + 1) -dimensional dispersive long water wave system is investigated. After travelling wave transformation, the governing model studied is converted into nonlinear ordinary differential equation. Some properties with the strain conditions are also reported. [ABSTRACT FROM AUTHOR]

The main purpose of the present investigation is to find the solution of fractional coupled equations describing the romantic relationships using q -homotopy analysis transform method (q -HATM). The considered scheme is a unification of q -homotopy analysis technique with Laplace transform (LT). More preciously, we scrutinized the behavior of the obtained solution for the considered model with fractional-order, in order to elucidate the effectiveness of the proposed algorithm. Further, for the different fractional-order and parameters offered by the considered method, the physical natures have been apprehended. The obtained consequences evidence that the proposed method is very effective and highly methodical to study and examine the nature and its corresponding consequences of the system of fractional order differential equations describing the real word problems. [ABSTRACT FROM AUTHOR]

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]