Abstract
Fractional calculus is a rising subject in the current research field. The researchers of different disciplines are using fractional calculus models to investigate different practical problems. In this paper, we found the exact solutions of space-time fractional generalized KdV equation, KdV Burger equation and Benjamin-Bona-Mahoney-Burgers equation with dual power-law nonlinearity. The solutions are expressed in terms of hyperbolic, trigonometric and rational functions.
Highlights
It is well known that to formulate the real world phenomenon most of the places non-linear integer order or fractional differential equations arise [1,2,3]
We found the exact solutions of space-time fractional generalized KdV equation, KdV Burger equation and Benjamin-Bona-MahoneyBurgers equation with dual power-law nonlinearity
The space-time fractional generalized KdV equation, KdV-Burger equation and Bona-Mahoney-Burgers equation with dual power-law nonlinearity first converted to integer order differential equation using the complex fractional transformation and those equations are solved using generalized Tanh method
Summary
It is well known that to formulate the real world phenomenon most of the places non-linear integer order or fractional differential equations arise [1,2,3]. In this paper we used the complex fractional transformation and generalized Tanh method to solve three non-linear space-time fractional differential equations arises in fluid dynamics and plasma dynamics. The space-time fractional generalized KdV equation, KdV-Burger equation and Bona-Mahoney-Burgers equation with dual power-law nonlinearity first converted to integer order differential equation using the complex fractional transformation and those equations are solved using generalized Tanh method. In this method the solutions are expressed in terms the hyperbolic, trigonometric and the rational functions. 5. Solution of Benjamin-Bona-Mahoney-Burgers equation with dual powerlaw nonlinearity using Generalized Tanh Method and complex fractional transformation. Comparing the coefficient of 0, 1, 2 and 3 from the equation (5.8) we get, Aa0 Aa1
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