Traveling wave solutions for (3+1) dimensional conformable fractional Zakharov-Kuznetsov equation with power law nonlinearity

Abstract

In this work, we consider the (3+1) dimensional conformable fractional Zakharov-Kuznetsov equation with power law nonlinearity. Solitary wave solutions, soliton wave solutions, elliptic wave solutions, and periodic (hyperbolic) wave rational solutions are obtained by means of the unified method. The solutions showed that this method provides us with a powerful mathematical tool for solving nonlinear conformable fractional evolution equations in various fields of applied sciences.

Constructions of the optical solitons and other solitons to the conformable fractional Zakharov–Kuznetsov equation with power law nonlinearity

“…To represent the idea of the modified (G /G)-expansion method [56], we apply the way on the (3 + 1)dimensional conformable fractional Zakharov-Kuznetsov equation with power law nonlinearity [28,46]. Let us consider that…”

“…Nonetheless, numerous applications have been executed in the economy, quantum field theory, optical fibres, plasma physics, fluid mechanics, mathematical physics, biology, geochemistry, to mention a few. Thus, various mathematical methods have been improved to answer them, such as Lie symmetry analysis [1], the auxiliary equation method [2], the FRDTM [3], the tanφ(ξ )/2)-expansion method [4], Tanh method [5], the Riccati-Bernoulli sub-ODE method [6], the exp−φ(ξ )-expansion method [7][8][9], extended trial equation method [10], Fractional Fan sub-equation method [11], new generalized (G /G)-expansion method [12][13][14][15], exponential rational function method [16], (G /G)-expansion method [17][18][19], modified extended tanh method [20], improved (G /G)expansion method [21], differential transform method [22], the Painleve analysis [23], fractional homotopy method [24], Truncation method [25], Semi-Inverse variational principle [26], the Feng's first integral method [27], the unified method [28], G G 2 -expansion method [29], singular manifold method [30], singular manifold method [31], homotopy perturbation transform method [32], Collocation method [33], separation of variables method [34], Lagrange multiplier method [35], fractional Adams-Bashforth-Moulton method [36], Chebyshev wavelet method [37], Jacobi elliptic function method …”

“…In this paper, the modified (G /G)-expansion process will obtain soliton answers of the following conformable fractional ZK model, including power law nonlinearity [28,46]. We are considering that using above model [28,46],…”

Fractional differential equations and Volterra–Stieltjes integral equations of the second kind

“…B Agnieszka B. Malinowska tional derivatives provide an excellent tool for the description of memory and hereditary properties of various materials and processes (Atanackovic and Stankovic 2009;Carpinteri and Mainardi 2014;Demir et al 2012;Kulish and Lage 2002;Meerschaert 2011;Podlubny 1999;Rezazadeh et al 2018;Tariq et al 2018;Vazquez 2005). Several types of fractional derivatives have been suggested to describe more accurately real-world phenomena, each one with their own advantages and disadvantages (Djida et al 2017;Kilbas et al 2006;Osman 2017;Osman et al 2019;Podlubny 1999;Rezazadeh et al 2019). A more general unifying perspective to the subject was proposed in Agrawal (2010), Klimek and Lupa (2013), Malinowska et al (2015), by considering fractional operators depending on general kernels.…”

Numerical solutions of fractional Boussinesq-Whitham-Broer-Kaup and diffusive Predator-Prey equations with conformable derivative

“…There are some common methods that are used to obtain approximate or analytical solutions of nonlinear fractional ordinary and partial differential equations in the literature [28,29,30,31,32,33,34,35,36,37]. These methods include, Laplace analysis method (LAM) [15] for the constant coefficient fractional differential equations, Adomian decomposition method (ADM) [13] for the dynamics of the fractional giving up smoking model of fractional order, homotopy perturbation method (HPM) [25] for the nonlinear fractional Schrödinger equation, homotopy analysis method (HAM) [18] for the conformable fractional Nizhnik-Novikov-Veselov system, differential transformation method (DTM) [19] for the convergence of fractional power series, Elzaki projected differential transform method [22] for system of linear and nonlinear fractional partial differential equations and perturbation-iteration algoritm (PIA) [20] for ordinary fractional differential equations.…”