Everything in a computer are discrete, not continuous (except the voltages on the chips themselves and the outputs of a soundcard or similar DAC transducers). So ‘continuous’ signals otherwise only exist in symbolic variables, not numeric arrays or vectors, since by definition those are all sampled.
The posted code is doing everything it should (or could) to represent the signal vectors correctly (although some variables appear to be missing).
y1_1 = (exp(abs(-0.5*t1))).*(2*sin(10*pi*t1)+cos(1*pi*t1));
y1_2 = (0.75).^abs(-t2+10);
y2_1 = (exp(abs(-0.5*(-t1-2)))).*(2*sin(10*pi*(-t1-2)))+cos(1*pi*(-t1-2));
y2_2 = (0.75).^abs(t2+12);
tconv = (t(1) +t(1):DT:t(end)+t(end));