On the Solution of Burgers’ Equation with the New Fractional Derivative

Abstract

Firstly in this article, the exact solution of a time fractional Burgers’ equation, where the derivative is conformable fractional derivative, with dirichlet and initial conditions is found byHopf-Cole transform. Thereafter the approximate analytical solution of the time conformable fractional Burger’s equation is determined by using a Homotopy Analysis Method(HAM). This solution involves an auxiliary parameter ~ which we also determine. The numerical solution of Burgers’ equation with the analytical solution obtained by using the Hopf-Cole transform is compared.

Keywords

• Hopf-Cole Transform
• Time Fractional Burgers’ Equation
• Conformable Fractional Derivative
• Time Fractional Heat Equation
• Homotopy Analysis Method