Soliton solutions of the conformable fractional Zakharov–Kuznetsov equation with dual-power law nonlinearity Farid Samsami Khodadad 1 • Fakhroddin Nazari 1 • Mostafa Eslami 2 • Hadi Rezazadeh 1 Received: 26 June 2017 / Accepted: 28 October 2017 Ó Springer Science+Business Media, LLC 2017 Abstract In this article, the Riccati sub equation method is employed to solve fractional Zakharov–Kuznetsov equation with dual-power law nonlinearity in the sense of the con- formable derivative. By using this method, new exact solutions involving parameters, expressed by generalized hyperbolic functions are obtained. This method presents a wider applicability for handling nonlinear fractional wave equations. Keywords Conformable fractional derivative  ZK Equation with dual-power law nonlinearity  Riccati-sub equation method 1 Introduction Fractional differential equations are the generalizations of classical differential equations with integer orders. In recent years, nonlinear fractional differential equations in mathe- matical physics are playing a major role in various fields of science and engineering, especially in mathematical physics, plasma physics, fluid dynamics, quantum field theory, chemical kinematics, chemical physics, propagation of shallow water waves and so on. The exact solutions of such equations are of fundamental importance since a lot of mathe- matical-physical models are described by nonlinear fractional evolution equations. A variety of powerful methods, such as, the first integral method (Aminikhah et al. 2015; Eslami et al. 2014), the G 0 /G-expansion method (Mirzazadeh et al. 2014; Bekir et al. 2015a), the Exp-function method (Talarposhti et al. 2016; Bekir et al. 2013), the Expo- nential rational function method (Aksoy et al. 2016), the ansatz method (Guner and Bekir & Mostafa Eslami Mostafa.eslami@umz.ac.ir 1 Faculty of Engineering Technology, Amol University of Special Modern Technologies, Amol, Iran 2 Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran 123 Opt Quant Electron (2017) 49:384 DOI 10.1007/s11082-017-1225-y