Exponentiation In PBC library I need to compute a function $h^l$, where h is an element of G2 and l is a rational number. How can this be done using the PBC library?

I have converted the h to an element in G2

As far as I have seen, for exponentiation, PBC has two functions :

element_pow_zn, and
element_pow_mpz


The first function is used when both the operands are of type element_t. The second function will be used when the power is of type mpz_t.

I read in the pbc manual that the mpz_t type is for integers in GMP, while mpq_t is for rationals. Can I use any of the functions in PBC to acquire the required exponentiation? If yes, how will I have to declare the elements?

UPDATE

Will such an initialization work :

mpz_t a, b, l;
element_t ea, eb, el, bi, t1, res;
....after computing a , b, I can use 
element_set_mpz(ea, a);
.
.

element_invert(bi, b);
element_pow_zn(t1, h, a);
element_pow_zn(res, t1, bi);
I don't think $h^l$ where l is a float number is a well defined operation in a finite group, regardless of what context you want to use this group for.
A group is a set of elements G with a binary operation $\cdot$ (multiplication) defined, often denoted as (G,$\cdot$) satisfying four properties. You can find more information here: http://mathworld.wolfram.com/Group.html.

Then, exponentiation is defined as repeating multiplication on a group element a certain number of times. For example, $h^n=h\cdot h\cdot h \cdot ... \cdot h$ (repeating $n$ times). So you should be able to see that for example repeating multiplication 3.1415956 times is not well defined.

Specifically, for pairing, G2 is a group over the twist curve. In this group, one operation is defined. Usually, this operation is called point addition. However, in PBC, if you look at the document, it is said that "The addition and multiplication functions perform addition and multiplication operations in rings and fields. For groups of points on an elliptic curve, such as the G1 and G2 groups associated with pairings, both addition and multiplication represent the group operation (and similarly both 0 and 1 represent the identity element). It is recommended that programs choose and one convention and stick with it to avoid confusion." (http://crypto.stanford.edu/pbc/manual/ch04s04.html).

So, the operation you are talking about is not well defined.