Lie symmetries and conservation laws for the time fractional Derrida–Lebowitz–Speer–Spohn equation

•By using the Lie group analysis method of fractional differential equations, we derive Lie symmetries for the time fractional Derrida–Lebowitz–Speer–Spohn (FDLSS) equation with Riemann–Liouville derivative.•In a particular case of scaling transformations, we transform the FDLSS equation into a nonlinear ordinary fractional differential equation.•Based on the new conservation laws theorem and the fractional generalization of the Noether operators, we derived conservation laws for the FDLSS equation.

This paper investigates the invariance properties of the time fractional Derrida–Lebowitz–Speer–Spohn (FDLSS) equation with Riemann–Liouville derivative. By using the Lie group analysis method of fractional differential equations, we derive Lie symmetries for the FDLSS equation. In a particular case of scaling transformations, we transform the FDLSS equation into a nonlinear ordinary fractional differential equation. Conservation laws for this equation are obtained with the aid of the new conservation theorem and the fractional generalization of the Noether operators.