Exact solutions of nonlinear fractional order partial differential equations via singular manifold method

• Published in: Chinese journal of physics (Taipei) Vol. 61; pp. 290 - 300
• Main Authors: Saleh, R., Kassem, M., Mabrouk, S.M.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.10.2019
• Subjects: Fractional complex transform; Painlevé analysis; Singular manifold method; Time fractional differential equation; Painlevé analysis; Singular manifold method; Fractional complex transform; Time fractional differential equation
• ISSN: 0577-9073
• DOI: 10.1016/j.cjph.2019.09.005

•Singular manifold method is applied to solve fractional equations.•Four distinct equations are attempted for traveling wave solutions.•Solutions include periodic kink, multi soliton and kink waves.•Singular manifold method is a powerful tool in fractional calculus. Singular manifold method is applied to solve nonlinear fractional partial differential equations (NLFPDEs). Fractional complex transformation is firstly used to reduce the equations to ordinary differential equations (ODEs). Using Bäcklund transformation the Schwarzian derivatives for the Eigen functions are obtained leading to a new variety of exact solutions. The method is applied to nonlinear time fractional Klein-Gordon, Cahn-Hilliard, Burger and Cahn-Allen equations. Some of the resulting solutions are graphically illustrated showing periodic kink, multi soliton and kink solutions.