Abstract
Abstract This paper proposes obtaining the new wave solutions of time fractional sixth order nonlinear Equation (KdV6) using sub-equation method where the fractional derivatives are considered in conformable sense. Conformable derivative is an understandable and applicable type of fractional derivative that satisfies almost all the basic properties of Newtonian classical derivative such as Leibniz rule, chain rule and etc. Also conformable derivative has some superiority over other popular fractional derivatives such as Caputo and Riemann-Liouville. In this paper all the computations are carried out by computer software called Mathematica.
Highlights
The number of studies on fractional partial differential equations have increased since they can be used in many fields such as physics, engineering, biology and chemistry [1,2,3]
Most of these studies focused on obtaining the exact solutions of fractional partial differential equations [13, 14]
It is not possible to solve some fractional derivatives by using these definitions
Summary
The number of studies on fractional partial differential equations have increased since they can be used in many fields such as physics, engineering, biology and chemistry [1,2,3]. Some of the fractional derivative definitions such as Riemann-Liouville and Caputo do not have capabilities to achieve the exact solutions. Because they do not satisfy some main principles of classical integer order derivative. Caputo and Riemann-Liouville derivatives do not satisfy the derivative of the quotient of two functions. The conformable fractional derivative has been used to provide new solutions for existing differential equations by many scientists. Ilie et al [5] studied general solutions of Riccati and Bernoulli fractional differential equations with conformable fractional derivative. Tasbozan and Kurt [12] obtained new travelling wave solutions of time-space fractional Liouville and Sine-Gordon equations using conformable fractional derivative definition. In this study authors aimed to find the new exact solutions of conformable time fractional (1+1) and (2+1) dimensional KdV6 equations [10, 11] with the aid of sub equation method
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