Lie symmetry analysis for fractional evolution equation with \(\zeta \)-Riemann–Liouville derivative

We present the application of Lie group theory analysis with \(\zeta \) $\zeta$ -Riemann–Liouville fractional derivative ( \(\zeta \) $\zeta$ -RLFD, for short) detailing the construction of infinitesimal prolongation to obtain Lie symmetries. In addition, it addresses the invariance condition without necessarily imposing that the lower limit of the fractional integral is fixed. We find an expression that expands the knowledge regarding the study of exact solutions for fractional differential equations. We apply the Leibniz-type rule for the derivative operator in question to build the prolongation. At last, we calculate the Lie symmetries of the generalized Burgers equation and fractional porous medium equation.