Abstract
In this article, an approximate analytical solution of fractional order nonlinear PDE’s with modified Riemann- Liouville derivative was obtained with the help of fractional variational iteration method (FVIM). It is showed that the solutions obtained by the FVIM are reliable and effective method for strongly nonlinear partial equations with modified Riemann-Liouville derivative. The solutions of our model equation can also be obtained from the known forms of the series solutions.
Highlights
It is known that various problems in electrical networks, control theory of dynamical systems, probability and statistics, electrochemistry of corrosion, chemical physics, optics, engineering, acoustics, material science and signal processing can be successfully modeled by linear or nonlinear fractional order differential equations
Fractional convection–diffusion equation with nonlinear source term solved by Momani and Yildirim [11], space–time fractional advection–dispersion equation by Yildirim and Kocak [12], fractional Zakharov–Kuznetsov equations by Yildirim and Gulkanat [13], integro-differential equation by El-Shahed [14], non-Newtonian flow by Siddiqui et al [15], fractional PDEs in fluid mechanics by Yildirim [16], fractional Schrödinger equation [17,18]
The aim of this paper is to extend the application of the variational iteration method method to solve fractional KDV, K(2,2), modified fractional KDV (mKDV) equation and some fractional partial equations in fluid mechanics with modified Riemann-Liouville derivative
Summary
It is known that various problems in electrical networks, control theory of dynamical systems, probability and statistics, electrochemistry of corrosion, chemical physics, optics, engineering, acoustics, material science and signal processing can be successfully modeled by linear or nonlinear fractional order differential equations. The variational iteration method (VIM), which proposed by JiHuan He [9], was successfully applied to autonomous ordinary and partial differential equations and other fields. The most recently, a new application of Fractional Variational Iteration Method (FVIM) for solving non-linear fractional coupled- KDV equations with modified Riemann-Liouville derivative performed by Merdan et al [32]. The aim of this paper is to extend the application of the variational iteration method method to solve fractional KDV, K(2,2), mKDV equation and some fractional partial equations in fluid mechanics with modified Riemann-Liouville derivative. To show in efficiency of this method, we give the implementation of the FVIM for the fractional KDV, K (2,2), mKDV equation and some fractional partial equations in fluid mechanics with modified Riemann-Liouville derivative and numerical results in Applications section.
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