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A unified explicit form for difference formulas to approximate the fractionaland classical derivatives is presented. The formula gives finite differenceapproximations for any classical derivatives with a desired order of accuracyat nodal point in the computational domain. It also gives Gr\"unwald typeapproximations for fractional derivatives with arbitrary order of approximationat any point. Thus, this explicit unifies approximations of both types ofderivatives. Moreover, for classical derivatives, it provides various finitedifference formulas such as forward, backward, central, staggered, compact,non-compact etc. Efficient computations of the coefficients of the differenceformulas are also presented that lead to automating the solution process ofdifferential equations with a given higher order accuracy. Some basicapplications are presented to demonstrate the usefulness of this unifiedformulation.

A unified explicit form for difference formulas for fractional and classical derivatives