Memristors are so much more interesting than the transistor replacements they're sometimes touted as. It feels as if they've been willed into existence just to make the mathematics of electronics more complete.
> The ideal memristor was initially and abstractly formulated as the flux–charge relationship: dΦ = M dq, (2) which, in order to be invertible, must have M defined either in terms of Φ, or q, or it must be a constant. The latter case coincides with the resistor, while if M is defined in terms of Φ ... [emphasis mine]
From my reading, this means if M is constant (like R,L,C are for "standard" components) it's just a resistor - not the miraculous "missing fourth."
Curious to get other perspectives on this.
To answer your question memristors cover the second case where the relationship isn't linear, thus tying the loose end resistors leave in the theory.