【 以下文字转载自 Physics 讨论区 】
发信人: chamberlain (PKU|PHY01|面朝大海|春暖花开), 信区: Physics
标 题: Re: How to calculate this derivative? (转载)
发信站: BBS 未名空间站 (Wed Dec 5 15:20:21 2007)
The original problem is to solve \phi(t) from
\int_0^z\phi(t) = \int_0^z f(x)(z-x)^{a-1} dx
where 0< a <1
I solved it in a general Laplace transform manner.
Perform Laplace transforms on both sides:
L[\int_0^z\phi(t)]
= 1/w L[\phi(t)]
L[ \int_0^z f(x)(z-x)^{a-1} dx ] (convolution)
= L[ x^{a-1} ] L[ f(x) ]
= w^{-a}\Gamma
