Integrodifferential equations of mixed type on time scales with Delta-HK and Delta-HKP integrals
| dc.contributor.author | Sikorska-Nowak, Aneta | |
| dc.date.accessioned | 2023-05-23T20:20:44Z | |
| dc.date.available | 2023-05-23T20:20:44Z | |
| dc.date.issued | 2023-03-14 | |
| dc.description.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. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 20 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.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. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/16864 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.holder | This work is licensed under a Creative Commons Attribution 4.0 International License. | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2022, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Integrodifferential equations | |
| dc.subject | Nonlinear Volterra integral equation | |
| dc.subject | Time scales | |
| dc.subject | Henstock-Kurzweil delta integral | |
| dc.subject | HL delta integral; Banach space | |
| dc.subject | Henstock-Kurzweil-Pettis delta integral | |
| dc.subject | Fixed point | |
| dc.subject | Measure of noncompactness | |
| dc.subject | Caratheodory solutions | |
| dc.subject | Pseudo-solution | |
| dc.title | Integrodifferential equations of mixed type on time scales with Delta-HK and Delta-HKP integrals | |
| dc.type | Article |