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In particular, the geometric and bigeometric calculi have been used extensively.
For more information, please see the Applications & Reception and Citations sections of this website. The six books on non-Newtonian calculus and related matters by Jane Grossman, Michael Grossman, and Robert Katz are indicated below, and are available at some academic libraries, public libraries, and booksellers such as (Please see item  in the References section.) Michael Grossman.
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(The geometric derivative and the bigeometric derivative are closely related to the well-known logarithmic derivative and elasticity, respectively.) The well-known arithmetic average (of functions) is the natural average in the classical calculus, but the well-known geometric average is the natural average in the geometric calculus.
And the well-known harmonic average and quadratic average (or root mean square) are closely related to the natural averages in the harmonic and quadratic calculi, respectively.
However, in the geometric calculus, the exponential functions are the functions having a constant derivative.
And in the bigeometric calculus, the power functions are the functions having a constant derivative.