Lie symmetry analysis, conservation laws and exact solutions of the seventh-order time fractional Sawada–Kotera–Ito equation

Abstract

a b s t r a c t 26 In this paper Lie symmetry analysis of the seventh-order time fractional Sawada-Kotera-Ito (FSKI) equa-27 tion with Riemann-Liouville derivative is performed. Using the Lie point symmetries of FSKI equation, it 28 is shown that it can be transformed into a nonlinear ordinary differential equation of fractional order 29 with a new dependent variable. In the reduced equation the derivative is in Erdelyi-Kober sense. 30 Furthermore, adapting the Ibragimov's nonlocal conservation method to time fractional partial differen-31 tial equations, we obtain conservation laws of the underlying equation. In addition, we construct some 32 exact travelling wave solutions for the FSKI equation using the sub-equation method.33

Symmetry Groups, Similarity Reductions, and Conservation Laws of the Time-Fractional Fujimoto–Watanabe Equation Using Lie Symmetry Analysis Method

“…is method is so effective. Researchers obtain analytical solutions and conservation laws to equations with the help of this method, for example, seventh-order time-fractional Sawada-Kotera-Ito equation, time-fractional fifth-order modified Sawada-Kotera equation, Burridge-Knopoff equation, and so on [33][34][35][36][37]. e time-fractional Fujimoto-Watanabe equation [38] is…”

q-Homotopy analysis method for solving the seventh-order time-fractional Lax’s Korteweg–de Vries and Sawada–Kotera equations

“…Some analytical methods used by different authors for solving the seventh-order Lax's Korteweg-de Vries and the Sawada-Kotera equations are the following: Adomian decomposition method (Adomian 1994;El-Sayed and Kaya 2004), pseudospectral method (Darvishi et al 2007), variational iteration method (Jafari et al 2008;Soliman 2006), and generalized Cole-Hopf transformation method (Salas and Gomez 2010). Yasar et al 2016 used lie symmetry analysis method to construct exact solutions to 7TfSK equation. InŞenol et al (2018), numerical solutions of the timefractional Rosenau-Hyman equation, which is a KdV-like model was examined using the residual power series method and perturbation-iteration algorithm.…”

Derivation of Direct Explicit Integrators of RK Type for Solving Class of Seventh-Order Ordinary Differential Equations

“…For example, the seventhorder Korteweg-de Vrie (KdV) is a nonlinear PDE, another application of seventh-order DE is nonlinear dispersive equations, which include several models arising in the study of different physical phenomena. For the review of the researches in seventh-order DEs [2], has studied an efficient numerical solution for seventhorder DEs by using septic B-spline collocation method while [3] has proposed a new method based on the Lengendre wavelets expansion together with operational matrices of fractional integration and derivative to solve time-fractional seventh-order KdV equation (sKdV) [4] has used differential transformation method for solving seventh-order BVPs [5] has solved the seventh -order ODEs by Haar wavelet approach [6] is performed Lie symmetry analysis of the seventh-order time fractional SawadaKoteralto (FSKI) equation with Remain-Liouville derivative [7], is employed the variational iteration method using Hes polynomials to solve the seventh-order boundary value problems (BVPs) and [8] is solved the Laxs seventh-order Korteweg-de Vires (KdV) equation by pseudospectral method. Moreover [17], is presented the numerical computations for waterbased nanofluids with A12O3 and Cu nanopar-ticles and [9] has introduced the numerical solution of a thermal instability problem in a rotating nanofluid layer [10,11] have derived direct explicit integrators for solving thirdorder ODEs.…”