Time Fractional Third-Order Evolution Equation: Symmetry Analysis, Explicit Solutions, and Conservation Laws

In this work, Lie symmetry analysis for the time fractional third-order evolution (TOE) equation with Riemann–Liouville (RL) derivative is analyzed. We transform the time fractional TOE equation to nonlinear ordinary differential equation (ODE) of fractional order using its Lie point symmetries with a new dependent variable. In the reduced equation, the derivative is in Erdelyi–Kober (EK) sense. We obtain a kind of an explicit power series solution for the governing equation based on the power series theory. Using Ibragimov's nonlocal conservation method to time fractional partial differential equations (FPDEs), we compute conservation laws (CLs) for the TOE equation. Two dimensional (2D), three-dimensional (3D), and contour plots for the explicit power series solution are presented.