Abstract
We consider the time-fractional thin-film equation with Riemann–Liouville derivative, which describes a lubrication theory model for the flow of thin viscous films with strong surface tension. Based on Lie symmetry analysis method, we derive the vector fields and optimal system of the equation, respectively. Using the resulting optimal system, we analyze the similarity reductions. Moreover, we obtain its power series solutions. Finally, by considering a new theorem of finding conservation laws, we derive the conservation laws associated with Lie symmetries of the equation.
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