Abstract
AbstractIn this paper, three eminent types of time-fractional nonlinear partial differential equations are considered, which are the fractional foam drainage equation, fractional Gardner equation, and fractional Fornberg–Whitham equation in the sense of conformable fractional derivative. The approximate solutions of these considered problems are constructed and discussed using the conformable fractional variational iteration method and conformable fractional reduced differential transform method. The conformable derivative is one of the admirable choices to handle nonlinear physical problems of different fields of interest. Comparisons of approximate solution obtained by two techniques, to each other and with the exact solutions are also presented and affirm that the considered methods are efficient and reliable techniques to study other nonlinear fractional equations and models in the sense of conformable derivative. To explain the effects of several parameters and variables on the movement, the approximate results are shown in tables and two-and three-dimensional surface graphs.
Highlights
Comparisons of approximate solution obtained by two techniques, to each other and with the exact solutions are presented and a rm that the considered methods are e cient and reliable techniques to study other nonlinear fractional equations and models in the sense of conformable derivative
Fractional partial di erential equations are used to model most of the natural problems, such as nance, physical, chemical, uid dynamics, biological and other elds of engineering
Conformable variational iteration method is built on the conformable derivative for fractional ordinary di erential equations and fractional partial di erential equations [21]
Summary
Fractional partial di erential equations are used to model most of the natural problems, such as nance, physical, chemical, uid dynamics, biological and other elds of engineering. The approximate solutions of these considered problems are constructed and discussed using the conformable fractional variational iteration method and conformable fractional reduced di erential transform method. Comparisons of approximate solution obtained by two techniques, to each other and with the exact solutions are presented and a rm that the considered methods are e cient and reliable techniques to study other nonlinear fractional equations and models in the sense of conformable derivative.
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