Optimum Solutions of Fractional Order Zakharov–Kuznetsov Equations

Abstract

In this paper, the Optimal Homotopy Asymptotic Method is extended to derive the approximate solutions of fractional order two-dimensional partial differential equations. The fractional order Zakharov–Kuznetsov equation is solved as a test example, while the time fractional derivatives are described in the Caputo sense. The solutions of the problem are computed in the form of rapidly convergent series with easily calculable components using Mathematica. Reliability of the proposed method is given by comparison with other methods in the literature. The obtained results showed that the method is powerful and efficient for determination of solution of higher-dimensional fractional order partial differential equations.

Numerical Investigation of Fractional‐Order Kawahara and Modified Kawahara Equations by a Semianalytical Method

“…Recently, Sarwar et al extended the idea of OHAM fractional-order partial differential equations and used them for different problems having fractional-order derivatives [27,28]. Nawaz et al applied the suggested approach to the fractional-order Zakharov-Kuznetsov equations [29]. Likewise, Zada et al…”

Analytical Solution of System of Volterra Integral Equations Using OHAM

“…Many researchers used the proposed technique for different types of problems in literature. Iqbal et al implemented it for Klein-Gordon equations [19] and singular Lane-Emden type equation [20], Sheikholeslami et al used OHAM for the investigation of the laminar viscous flow [21], Hashmi et al obtained solution of Fredholm integral equations [22], and Nawaz et al obtained optimum solutions of fractional-order Zakharov-Kuznetsov Equations [23], three-dimensional Volterra integral equations [24], and fractional integro-differential equations [25]. We apply the method to obtain the approximate solution of a system of VIEs and test some numerical examples to show the effectiveness and accuracy of the method.…”