Solving Fractional Exponent with Elementary Laplace

[2RIP]

Hi

Homework Statement

L[f] = (s)^(1/2)

The Attempt at a Solution

Is there actually an elementary laplace transform that can compute this? I tried using derivative to solve for it, but i'll always be stuck with a fractional exponent.

Thanks

 

[jhicks]

The best thing I could think of is using the convolution rule, i.e. (F(s)G(s) = f(t)*g(t)) where * is convolution. Let F(s)=G(s)=s^(1/2), then F(s)G(s) = s. Can you do the laplace transform of s?

 

[2RIP]

Oh, our class hasn't got to that section yet. Maybe I'll be able to solve it tomorrow then. Thanks.

 

[2RIP]

I think i might have just thought of something. Would it work if i first took the derivative. Then used the gamma function to compute the inverse laplace transform?

 

[jhicks]

The gamma function isn't in a form that is immediately obvious to me to see how it relates to what you have to evaluate.