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The solution of the Lax tensor equations in the case L[sub αβγ]= -L[sub βαγ] was analyzed. The Lax tensors on the dual metrics were investigated. We classified all two-dimensional metrics having the symmetric Lax tensor L[sub αβγ]. The Lax tensors of the flat space, Rindler system and its dual were found. [ABSTRACT FROM AUTHOR]

In this paper, the fractional reduced differential transform method (FRDTM) is used to obtain the series solution of time-fractional seventh-order Sawada–Kotera (SSK) and Lax's KdV (LKdV) equations under initial conditions (ICs). Here, the fractional derivatives are considered in the Caputo sense. The results obtained are contrasted with other previous techniques for a specific case, α = 1 revealing that the presented solutions agree with the existing solutions. Further, convergence analysis of the present results with an increasing number of terms of the solution and absolute error has also been studied. The behavior of the FRDTM solution and the effects on different values α are illustrated graphically. Also, CPU-time taken to obtain the solutions of the title problems using FRDTM has been demonstrated. [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]

In this work, a new modified fractional form of the Nagumo equation has been presented and deeply analyzed. Using the Caputo–Fabrizio and Atangana–Baleanu time-fractional derivatives, classical Nagumo model is transformed to a new fractional version. The modified equation has been solved by using the homotopy analysis transform method. The convergence analysis has been also examined with the help of the so-called h -curves and average residual error. Comparing the obtained approximate solution with the exact solution leaves no doubt believing that the proposed technique is very efficient and converges toward the exact solution very rapidly. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the q -Shehu transform. Further, we define the generalized hyper-Bessel function. Also, we state the q -Shehu transform for some elementary functions. The present aim in this paper is to obtain the solutions of the q -fractional kinetic equations in terms of the established generalized hyper-Bessel function by applying the established q -Shehu transform. Also, we give some special cases of our main results. At the end of this paper, we give the numerical values and the graphical representations of these solutions by using the software MATLAB. [ABSTRACT FROM AUTHOR]

This paper presents the modulation instability (MI) analysis and the different types of optical soliton solutions of the Triki–Biswas model equation. The aforesaid model equation is the generalization of the derivative nonlinear Schrödinger equation which describes the ultrashort pulse propagation with non-Kerr dispersion. The study is carried out by means of a novel efficient integration scheme. During this work, a sequence of optical solitons is produced that may have an important in optical fiber systems. The results show that the studied model hypothetically has incredibly rich optical soliton solutions. The constraint conditions for valid soliton solutions are also reported. The gained results show that the applied method is efficient, powerful and can be applied to various complex models with the help of representative calculations. [ABSTRACT FROM AUTHOR]

In this paper, the Homotopy perturbation Laplace method is implemented to investigate the solution of fractional-order Whitham–Broer–Kaup equations. The derivative of fractional-order is described in Caputo's sense. To show the reliability of the suggested method, the solution of certain illustrative examples are presented. The results of the suggested method are shown and explained with the help of its graphical representation. The solutions of fractional-order problems as well as integer-order problems are determined by using the present technique. It has been observed that the obtained solutions are in significant agreement with the actual solutions to the targeted problems. Computationally, it has been analyzed that the solutions at different fractional-orders have a higher rate of convergence to the solution at integer-order of the derivative. Due to the analytical analysis of the problems, this study can further modify the solution of other fractional-order problems. [ABSTRACT FROM AUTHOR]