Integrodifferential equations of mixed type on time scales with -hk and -hkp integrals

In this article we prove the existence of solutions to the integrod-ifferential equation of mixed type x(Delta)(t) = f (t, x(t), integral(t)(0)k(1) (t, s)g (s, x(s))Delta s; integral(a)(0) k(2)(t, s)h(s, x(s))Delta s), x(0) = x(0); x0 is an element of E; t is an element of I-a = [0, a] boolean AND T, a > 0, where T denotes a time scale (nonempty closed subset of real numbers R), I-a is a time scale interval. In the first part of this paper functions f, g, h are Caratheodory functions with values in a Banach space E and integrals are taken in the sense of Henstock-Kurzweil delta integrals, which generalizes the Henstock-Kurzweil integrals. In the second part f, g, h, x are weakly-weakly sequentially continuous functions and integrals are taken in the sense of Henstock-Kurzweil-Pettis delta integrals. Additionally, functions f, g, h satisfy some boundary conditions and conditions expressed in terms of measures of noncompactness.