Lie symmetries, conservation laws and exact solutions for time fractional Ito equation

Abstract

In this study, lie symmetry analysis, conservation theorem and improved fractional sub-equation method are discussed. The given methods are applied to the time fractional Ito equation. Firstly, we found Lie symmetries of the Ito equation and the given equation is reduced to fractional ordinary differential equation with the help of Erdélyi–Kober fractional differential operator and Erdélyi–Kober fractional integral operator. Conservation laws are obtained. Finally, we obtained the exact solutions of the Ito equation in the form of hyperbolic, trigonometric, rational functions. We obtained the solutions with the help of the improved fractional sub-equation method.

Keywords:

• Fractional differential equations
• fractional lie group method
• lie symmetries

MSC(2010):

• 35R11
• 70S10
• 76M60