3
$\begingroup$

Mathematica seems not to to know the basic Laplace and inverse Laplace relation

$$\mathcal L(E_\alpha[−λt^α],t)(s)=\frac{s^{α-1}}{λ+s^α}$$

surrounding the Mittag Leffler function (MittagLefflerE). The evaluations

LaplaceTransform[MittagLefflerE[alpha, -lambda t^alpha], t, s]

Integrate[ Exp[-s t] MittagLefflerE[alpha, -lambda t^alpha], {t, 0, Infinity}]

InverseLaplaceTransform[s^(alpha - 1)/(lambda + s^alpha), s, t]

1/(2*Pi*I)* Integrate[ Exp[s t] s^(alpha - 1)/(lambda + s^alpha), {s, -Infinity, Infinity}] 

all fail. However, when setting $\alpha=1$ the correct Laplace transform $1/(\lambda +s)$ of the expontential function is recovered.

Has anybody had more success with this kind computations?

$\endgroup$
  • $\begingroup$ It seems to me that the current symbolic support for general Mittag-Leffler functions is quite limited. $\endgroup$ – J. M. will be back soon May 12 '17 at 12:31
1
$\begingroup$

It seems to be an unsupported feature indeed. I received this answer from Wolfram Research in the discussion pages:

https://community.wolfram.com/groups/-/m/t/1090476

Thank your these examples.

The failure of LaplaceTransform and other functions to evaluate for MittagLefflerE in your examples is a limitation that we hope to address in a future release.

I apologize for the inconvenience caused by this limitation.

Sincerely, Devendra Kapadia, Wolfram Research, Inc.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.