A unified Explicit form for difference formulas for fractional and classical derivatives and applications

A unified explicit form for difference formulas to approximate the fractional and classical derivatives is presented.
The formula gives finite difference approximations for any classical derivative with a desired order of accuracy
at any nodal point in the computational domain. It also gives Grunwald type approximations for fractional
derivatives with arbitrary order of approximation at any point. Thus, this formulation unifies approximations
of both types of derivatives. Moreover, classical derivatives, provide various finite difference formulas such as
forward, backward, central, staggered, compact, non-compact, etc. Efficient computations of the coefficients of
the difference formulas are also presented which leads to automating the solution process of differential equations
with a given higher-order accuracy. Some basic applications are presented to demonstrate the usefulness of this
unified formulation.