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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 Δ T , then  g ( f ( t )) is Grünwald-Letnikov differintegral of that sequence with an order closely related to  dt  and Δ T . 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.

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