Editing Integral equation (section)

=== Integro-differential equations ===
An [[Integro-differential equation|Integro-differential]] equation, as the name suggests, combines differential and integral operators into one equation.<ref name=":0" /> There are many version including the Volterra integro-differential equation and delay type equations as defined below.<ref name=":2" /> For example, using the Volterra operator as defined above, the Volterra integro-differential equation may be written as:<ref name=":2" /><math display="block">y'(t)=f(t, y(t))+(V_\alpha y)(t)</math>For delay problems, we can define the delay integral operator <math>(\mathcal{W}_{\theta , \alpha} y)</math> as:<ref name=":2" /><math display="block">(\mathcal{W}_{\theta , \alpha} y)(t) := \int_{\theta(t)}^t (t-s)^{-\alpha} \cdot k_2(t,s,y(s), y'(s)) \, ds  </math>where the delay integro-differential equation may be expressed as:<ref name=":2" />
<math display="block">y'(t)=f(t, y(t), y(\theta (t)))+(\mathcal{W}_{\theta , \alpha} y)(t).</math>