Laplace inversion for fractional-order transfer functions

I am using the FOMCON toolbox, which enables me to introduce transfer functions with a fractional order. However, when I want to use the laplace inversion function, it works for simple cases but not for a bit complicated equations. Can anyone help me with this?

Example 1: works

syms s
TF = 1/s^0.5;
ilaplace(TF)

ans = 
    1/(t^(1/2)*pi^(1/2))

Example 2: does not work (only works when a = integer)

syms s
a = 0.5
TF = 1/(5 + (3*(s^a + (1/2^a)))/(s^a + (1/6^a)));
ilaplace(TF)

answ = 
    ilaplace(1/(((3*2^(1/2))/2 + 3*s^(1/2))/(6^(1/2)/6 + s^(1/2)) + 5), s, t)        

Answer 1

[Patel Mounika]

The ilaplace function of the symbolic engine currently does not implement an explicit expression for

ilaplace(1/(5 + (3*(s^a + (1/2^a)))/(s^a + (1/6^a)))) if a is not an integer .

The ilaplace function computes the analytic closed inverse Laplace form of a transfer function. It seems that mathematically a closed inverse Laplace form for 1/(5 + (3*(s^a + (1/2^a)))/(s^a + (1/6^a))) for general a cannot be found out, so ilaplace function will not simplify it further.

Nevertheless, there is a community submission at MathWorks File Exchange which numerically approximates an inverse Laplace transform for any function of "s". Following is the link of the same:

https://www.mathworks.com/matlabcentral/fileexchange/39035-numerical-inverse-laplace-transform/