New analytical solutions of the space fractional KdV equation in terms of Jacobi elliptic functions

Abstract

Abstract:In this study, new families of analytical exact solutions of the space fractional Korteweg-de Vries (KdV) equation are presented. Here, the fractional derivative is considered in conformable sense. By utilizing the Jacobi elliptic function expansion method, the solutions are obtained in general form containing the hyperbolic, trigonometric, and rational functions. Also, the complex valued solutions are obtained and some solutions of this equation are demonstrated.

Jacobi Elliptic Function Solutions of Space-Time Fractional Symmetric Regularized Long Wave Equation

“…Some of them are seen in Ref. [32][33][34][35][36]. The Jacobi elliptic function solutions of Eq.…”

Exact solutions of time fractional Korteweg–de Vries–Zakharov–Kuznetsov equation

“…The analytic method for this equation is not yet available in the literature. On the other side, in order to gain the exact solutions of different conformable fractional partial differential equations, Jacobi elliptic functions have been utilized in pervious works 17–20 . For the suggested method, the derivative using in Equation does not need to be conformable.…”

Diverse Soliton Structures for Fractional Nonlinear Schrodinger Equation, KdV Equation and WBBM Equation Adopting a New Technique

“…Instantly, the fractional nonlinear Schrodinger equation has been demonstrated by Hemida et al, (2012) via homotopy analysis method and found few series solutions [32]; the same equation for = 1 has been considered by and found three analytic solutions only by using the ( ′ / , 1/ )-expansion method and one solution by the (1/ ′)-expansion method [33]; arbitrary order nonlinear Schrodinger equation has been studied through fractional Riccati expansion method and achieved four exact wave solutions by Salam et al [34]; the new type F-expansion method has been applied to construct exact solutions of the space-time fractional cubic Schrodinger equation by Pandir and Duzgun [35]; Wazwaz and Kaur have used variational iteration method and improved ( ′ / )expansion method which left several solutions to the integer order cubic Schrodinger equation [36]; Cheema and Younis have considered the same equation for = 1 and obtained sixteen solutions by the extended Fan sub-equation method [37]; have investigated the equation of integer order by new auxiliary equation method and found soliton types solutions [38]. The conformable space-time fractional KdV equation has been studied by Yaslan and Girgin (2019) via the ( ′ / 2 )-expansion method for analytic wave solutions [39]; Odibat (2017) has employed Riccati equation approach to the KdV equation and constructed wave solutions [40]; the local variational iteration method and the local fractional series expansion method has been adopted by Jasim and Baleanu (2019) to study the fractional KdV equation [41]; Liu and Zhang (2018) have investigated the same equation by improved ( ′ / )-expansion method and found exact analytic solutions [42]; Jacobi elliptic function expansion method has been assumed to examine the KdV equation by Dascioglu et al (2017) [43]. Akram et al (2021) have studied the fractional Wazwaz-Benjamin-Bona-Mahony by extended modified auxiliary equation mapping method which left different soliton types solutions [44]; the same equation has been explored by Seadawy et al (2019) with the help of simple ansatzs and gained hyperbolic function and periodic function solutions [45].…”