Integrodifferential equations of mixed type on time scales with Delta-HK and Delta-HKP integrals
Date
2023-03-14
Authors
Sikorska-Nowak, Aneta
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In 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.
Description
Keywords
Integrodifferential equations, Nonlinear Volterra integral equation, Time scales, Henstock-Kurzweil delta integral, HL delta integral; Banach space, Henstock-Kurzweil-Pettis delta integral, Fixed point, Measure of noncompactness, Caratheodory solutions, Pseudo-solution
Citation
Sikorska-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.
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Attribution 4.0 International
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This work is licensed under a Creative Commons Attribution 4.0 International License.