Sikorska-Nowak, Aneta2023-05-232023-05-232023-03-14Sikorska-Nowak, A. (2023). Integrodifferential equations of mixed type on time scales with Delta-HK and Delta-HKP integrals. <i>Electronic Journal of Differential Equations, 2023</i>(29), pp. 1-20.1072-6691https://hdl.handle.net/10877/16864In this article we prove the existence of solutions to the integrodifferential equation of mixed type xΔ(t) = ƒ(t, x(t), ∫t0 k1 (t, s)g(s, x(s))Δs, ∫α0 k2 (t, s)h(s, x(s))Δs), x(0) = x0, x0 ∈ E, t ∈ Iα = [0, α] ∩ T, α > 0, where T denotes a time scale (nonempty closed subset of real numbers ℝ), Ia 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.Text20 pages1 file (.pdf)enAttribution 4.0 InternationalIntegrodifferential equationsNonlinear Volterra integral equationTime scalesHenstock-Kurzweil delta integralHL delta integral; Banach spaceHenstock-Kurzweil-Pettis delta integralFixed pointMeasure of noncompactnessCaratheodory solutionsPseudo-solutionArticleThis work is licensed under a Creative Commons Attribution 4.0 International License.