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The novel wave profiles for the more general (2 + 1) -dimensional Boussinesq equation are established in this paper. To get such outstanding results, we employ the potent Sardar sub-equation technique. The recognized explanations for several physical difficulties have been studied. These technological advancements have been proven to be helpful for the transmission of long-wave and high-power communications networks. The circumstances that gave rise to the emergence of these solutions are described in detail. The physical characteristics of the governing equation have been depicted in contour plots and three dimensions. [ABSTRACT FROM AUTHOR]

This study focuses on the analytical and numerical solutions of the convexity analysis for fractional differences with exponential and Mittag-Leffler kernels involving negative and nonnegative lower bounds. In the analytical part of the paper, we will give a new formula for ∇ 2 of the discrete fractional differences, which can be useful to obtain the convexity results. The correlation between the nonnegativity and negativity of both of the discrete fractional differences, ( a CFR ∇ α f) (t) and ( a ABR ∇ α f) (t) , with the convexity of the functions will be examined. In light of the main lemmas, we will define the two decreasing subsets of (2 , 3) , namely ℋ k , and ℳ k , . The decrease of these sets enables us to obtain the relationship between the negative lower bound of ( a CFR ∇ α f) (t) and the convexity of the function on a finite time set given by N a + 1 P : = { a + 1 , a + 2 , ... , P } , for some P ∈ N a + 1 : = { a + 1 , a + 2 , ... }. Besides, the numerical part of the paper is dedicated to examine the validity of the sets ℋ k , and ℳ k , in certain regions of the solutions for different values of k and . For this reason, we will illustrate the domain of the solutions by means of several figures in which the validity of the main theorems are explained. [ABSTRACT FROM AUTHOR]

In this paper, new analytical obliquely propagating wave solutions for the time fractional extended Zakharov–Kuzetsov (FEZK) equation of conformable derivative are investigated. By using the main properties of the conformable derivative, the FEZK equation is transformed into integer-order differential equations, and the reduced equations are solved via the generalized exponential rational function method (GERFM). The shape and features for the resulting solutions are illustrated through three-dimensional (3D) plots and corresponding contour plots for various values of the free parameters. [ABSTRACT FROM AUTHOR]