Lie Symmetries With Exact Solution for Time‐Fractional Foam Drainage Equation

ABSTRACT In this article, we consider a nonlinear time‐fractional foam drainage equation and investigate the behavior of fluid flow through the foam. First, we apply the symmetry analysis and obtain the infinitesimal group of transformations involving some arbitrary parameters. Further, we classify the one‐dimensional optimal algebra, and using that, we obtain the similarity variables, which consequently reduces the time fractional partial differential equation (FPDE) to fractional‐order ordinary differential equation (FODE). Next, under the invariance condition, we construct exact solution for the given model and presented graphically. Furthermore, we derive the two‐dimensional optimal systems and nonclassical symmetry for the governing equation. Finally, we study the nature of fluid flow through the foam by numerical simulation.