QUALITATIVE PROPERTIES OF THE SOURCE-FREE CAPUTO TIME-FRACTIONAL NONLINEAR FILTRATION EQUATION

Аннотация

The nonlocal character of the Caputo time-fractional nonlinear filtration equation, which
accounts for memory effects, complicates the search for an exact solution. In this paper, the equation is
studied through a leading-order self-similar simplification, which reduces it to an ordinary differential
equation admitting an exact solution in terms of the incomplete beta function. The obtained results are
compared with the rigorous theory based on the full Erdélyi–Kober operator, and by demonstrating the
dominance of the neglected term near the free boundary, it is proved that the critical condition and the free
boundary exponent belong not to the original equation but to the applied approximation itself.