  Universal difference quotient representations are introduced for the exact
self-sameness principles (SSP) as rules for rates of change introduced in
[Clemence-Mkhope, D.P (2021, Preprint). The Exact Spectral Derivative
Discretization Finite Difference (ESDDFD) Method for Wave Models. arXiv].
Properties are presented for the fundamental rule, a generalized derivative
representation which is shown to yield some known non-integer derivatives as
limit cases of such natural derivative measures; this is shown for some local
derivatives of conformable, fractional, or fractal type and non-local
derivatives of Caputo and Riemann-Liouville type. The SSP-inspired exact
spectral derivative discretization finite difference method is presented for
the Fokker-Planck non-fractional and time-fractional equations; the resulting
discrete models recover exactly some known behaviors predicted for the
processes modeled, such as the Gibbs-Boltzmann distribution and the
Einstein-Stokes-Smoluchowski relation; new ones are predicted.
