rosana
What is the delta-derivative of f(t)=t^2 with definition?
Time scale calculus
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replied to: rosana
Mdrafzi
Replied to: What is the delta-derivative of f(t)=t^2 with definition?
F(t)=t^2
f^nabla (t)=(f(sigma(t))-f(t))/(sigma(t)-t)
=(sigma^2 (t)-t)/(sigma(t)-t)
=(sigma(t)-t)(sigma(t)+t)/(sigma(t)-t)
=sigma(t)+ t,
where sigma(t) is the forward jump operator.
f^nabla (t)=(f(sigma(t))-f(t))/(sigma(t)-t)
=(sigma^2 (t)-t)/(sigma(t)-t)
=(sigma(t)-t)(sigma(t)+t)/(sigma(t)-t)
=sigma(t)+ t,
where sigma(t) is the forward jump operator.