Derivative
Take a function:
- ,
(where R could be any Banach space, but set it to be the real line for simplicity).
Definition: The delta derivative (also Hilger derivative) exists if and only if:
For every there exists a neighborhood of such that:
for all in .
Take Then, ; is the derivative used in standard calculus. If (the integers), is the forward difference operator used in difference equations.
Read more about this topic: Time-scale Calculus
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