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 by Hopf-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.

General solution of second order fractional differential equations

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