Classical and nonclassical Lie symmetry analysis to a class of nonlinear time-fractional differential equations

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• 作者：R. Najafi ; F. Bahrami ; M. S. Hashemi
• 关键词：Classical and nonclassical Lie symmetry analysis ; Time ; fractional differential equations ; Fractional diffusion ; Burger’s ; Airy’s ; KdV ; gas dynamic ; Fisher’s equation
• 刊名：Nonlinear Dynamics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：87
• 期：3
• 页码：1785-1796
• 全文大小：
• 刊物类别：Engineering
• 刊物主题：Vibration, Dynamical Systems, Control; Classical Mechanics; Mechanical Engineering; Automotive Engineering;
• 出版者：Springer Netherlands
• ISSN：1573-269X
• 卷排序：87

文摘

This study is devoted to a class of linear and nonlinear differential equations with fractional-order governing diffusion, Burger’s, Airy’s, KdV, gas dynamic and Fisher’s equations. These equations are used to describe the physical processes of models possessing memory. By employing classical and nonclassical Lie symmetry analysis and some technical calculations, new infinitesimal generators are obtained which give rise to derive the invariant solutions for this class of equations.