Convolution integral equation ode15s

I am solving a DAE system in Matlab using the ode15s suite. I'd like to add a further equation that I found in literature which reads:

R and F are two of the functions I am already integrating in the system and they are both dependent on the time t only, while x and y should be dummy integration variables.

I can't numerically calculate the integrals because it would need all the previos values of R and F in time, to which I have not access from within the function.

I also don't know how to correctly perform a time derivative of such a kind of equation.

If anyone has faced this problem already, it would be great to have som feedback from him/her. Thanks.

P.S.: since I am not familiar with this problem at all, please feel free to suggest more appropriate question's title and tags.

[Torsten]

What do you insert for x as lower limit of integration for the integral in the denominator ?

[Davide Masiello]

Hi Torsten.

Since x is the integration variable of the outer integral I assumed that, for any time t, x spans from 0 to t. I am not totally sure of this, but it is also the only option that makes sense to me. In all the references I found, both x and y appear only within those integrals (i.e. they are not defined anywhere else in the system) and therefore I don't think they have any physical meaning.

[Torsten]

I don't think that it is possible to write an ODE for T_li(t) that can be solved simultaneously with the ones for R and F.

You should calculate T_li(t) with the discrete data for R and F after integration using "interp1" for interpolation and "integral".