ternary operator doesn't work with lambda functions

The second and third operands of the conditional operator must have the same type or there must be some common type to which they can both be converted that the compiler can figure out. There are only a handful of conversions that the compiler will consider.

Your two lambda expressions have different types, and there is no common type to which they can both be converted (conversions to user-defined types, like std::function<double()>, cannot be considered because there are potentially an infinite number of valid target types).

You can directly convert each of the operands to std::function<double()>:

k.*variable = fn_type==exponential
    ? std::function<double()>([=,&k](){ return initial*exp(-k.kstep*par); })
    : std::function<double()>([=,&k](){ return initial*pow(k.kstep, par); });

But really, it's cleaner with the if/else.