Physical and Geometrical Interpretation of Grünwald-Letnikov Differintegrals: Measurement of Path and Acceleration

Abstract

Abstract A function f(t) of the independent variable t changing with every increment dt can be formulated as a functional sequence. If g(f(t)) is a derivative or an integral of f(t) and the value of dt is interpreted subject to an error ΔT, then g(f(t)) is Grünwald-Letnikov differintegral of that sequence with an order closely related to dt and ΔT. This paper illustrates this relationship and proposes a geometrical and physical interpretation of a fractional order Grünwald-Letnikov differintegrals using the example of path and acceleration measurements of a point in motion.