- #1
Hoplite
- 51
- 0
I have the problem,
[tex]ty(t)= \int_{0}^{t}\tau^{\alpha-1}y(t-\tau)d\tau[/tex]
subject to the constraint that [tex]\int_{0}^{\infty}y(t)dt=1[/tex].
In need to get the answer in the form of, Y(p)=something (where Y(p) is the Laplace transform of y(t)).
I can see that the right hand side is [tex]Y(p)\frac{\Gamma(\alpha)}{p^a}[/tex], but how could I evaluate the left hand side?
[tex]ty(t)= \int_{0}^{t}\tau^{\alpha-1}y(t-\tau)d\tau[/tex]
subject to the constraint that [tex]\int_{0}^{\infty}y(t)dt=1[/tex].
In need to get the answer in the form of, Y(p)=something (where Y(p) is the Laplace transform of y(t)).
I can see that the right hand side is [tex]Y(p)\frac{\Gamma(\alpha)}{p^a}[/tex], but how could I evaluate the left hand side?