{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:07:30Z","timestamp":1760058450512,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,4,1]],"date-time":"2025-04-01T00:00:00Z","timestamp":1743465600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministry of Science and Technological Development, Republic of Serbia","award":["451-03-68\/2020\/14\/200156"],"award-info":[{"award-number":["451-03-68\/2020\/14\/200156"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The main aim of this paper is to investigate the existence and uniqueness of solutions for some classes of abstract degenerate non-scalar Volterra equations on the line. In order to achieve our aims, we essentially apply the vector-valued Fourier transform. We use the class of (A,k,B)-regularized C-pseudoresolvent families in our analysis as well, and present several useful remarks and illustrative applications of the established results.<\/jats:p>","DOI":"10.3390\/axioms14040266","type":"journal-article","created":{"date-parts":[[2025,4,1]],"date-time":"2025-04-01T11:08:40Z","timestamp":1743505720000},"page":"266","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Abstract Degenerate Non-Scalar Volterra Equations on the Line"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0392-4976","authenticated-orcid":false,"given":"Marko","family":"Kosti\u0107","sequence":"first","affiliation":[{"name":"Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovi\u0107a 6, 21125 Novi Sad, Serbia"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Pr\u00fcss, J. (1993). Evolutionary Integral Equations and Applications, Birkh\u00e4user-Verlag.","DOI":"10.1007\/978-3-0348-8570-6"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Fedorov, V.E., and Skripka, N.M. (2024). Evolution equations with Liouville derivative on R without initial conditions. Mathematics, 12.","DOI":"10.3390\/math12040572"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1007\/s00233-013-9474-y","article-title":"Bounded mild solutions to fractional integrodifferential equations in Banach spaces","volume":"87","author":"Ponce","year":"2013","journal-title":"Semigroup Forum"},{"key":"ref_4","unstructured":"Kosti\u0107, M. (2025, March 02). Abstract Volterra Integro-Differential Inclusions with Generalized Weyl Fractional Derivatives. Submitted. Available online: https:\/\/www.researchgate.net\/publication\/388819627."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"617","DOI":"10.1007\/s40590-019-00239-1","article-title":"Differential and integral equations for the Laguerre\u2013Gould\u2013Hopper-based Appell and related polynomials","volume":"26","author":"Wani","year":"2020","journal-title":"Bol. Soc. Mat. Mex."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1515\/gmj-2019-2028","article-title":"Fractional calculus and generalized forms of special polynomials associated with Appell sequences","volume":"28","author":"Khan","year":"2021","journal-title":"Georgian Math. J."},{"key":"ref_7","unstructured":"Kosti\u0107, M. (2020). Abstract Degenerate Volterra Integro-Differential Equations, Mathematical Institute SANU."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Arendt, W., Batty, C.J.K., Hieber, M., and Neubrander, F. (2001). Vector-Valued Laplace Transforms and Cauchy Problems, Birkh\u00e4user. Monographs in Mathematics.","DOI":"10.1007\/978-3-0348-5075-9"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Carmichael, R.D. (2022). Cauchy integral and boundary value for vector-valued tempered distributions. 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An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley."},{"key":"ref_14","unstructured":"Samko, S.G., Kilbas, A.A., and Marichev, O.I. (1987). Fractional Integrals and Derivatives: Theory and Applications, Nauka i Tehnika. (In Russian)."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Kosti\u0107, M. (2024). Multidimensional fractional calculus: Theory and applications. Axioms, 13.","DOI":"10.3390\/axioms13090623"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Lighthill, M.J. (1959). Introduction to Fourier Transform and Generalised Functions, Cambridge University Press.","DOI":"10.1017\/CBO9781139171427"},{"key":"ref_17","unstructured":"Kosti\u0107, M. (2011). Generalized Semigroups and Cosine Functions, Mathematical Institute SANU."},{"key":"ref_18","first-page":"1","article-title":"Multipliers and convolutors in the space of tempered ultradistributions","volume":"44","author":"Dimovski","year":"2014","journal-title":"Novi Sad J. Math."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1007\/BF02395468","article-title":"Zur theorie der fastperiodischen Funktionen I","volume":"45","author":"Bohr","year":"1924","journal-title":"Acta Math."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1007\/BF02543859","article-title":"Zur theorie der fastperiodischen Funktionen II","volume":"16","author":"Bohr","year":"1925","journal-title":"Acta Math."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1007\/BF02543846","article-title":"Zur theorie der fastperiodischen Funktionen III","volume":"HT","author":"Bohr","year":"1926","journal-title":"Acta Math."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Kosti\u0107, M. (2019). Almost Periodic and Almost Automorphic Type Solutions to Integro-Differential Equations, W. de Gruyter.","DOI":"10.1515\/9783110641851"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Kosti\u0107, M. 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