The fractional calculus is partly about nested indefinite integrals. Is there any study or body of knowledge on nested DEFINITE integrals? For example, the fractional calculus helps with this integral: $\int_0^{l_2}{\left(\int_0^{l_1}{f(l_1)dl_1}\right)dl_2}$ It can be readily observed that these forms don't allow for any limits of integration other than a new variable to replace the previous variable of integration.
What I am looking for is nested integrals that have functions for the limits of integration: $\int_{g_2(x_1,x_2,\dots,x_n)}^{f_2(x_1,x_2,\dots,x_n)}{\left(\int_{g_1(x_1,x_2,\dots,x_n)}^{f_1(x_1,x_2,\dots,x_m)}{f(x_1,x_2,\dots,x_m)dx_i}\right)dx_j}$
Where or how can I find more about this second form of nesting?
REFINEMENT
The first expression above is combined into an operator, say $J$, to the second power in the fractional calculus. I'm looking for an extension of this so that the second expression can be combined into a similar operator, say $J_2$. I'm wondering where this has been done. It seems to be more than just iterated integrals.