{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,12]],"date-time":"2026-06-12T07:54:44Z","timestamp":1781250884022,"version":"3.54.1"},"reference-count":56,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2024,9,12]],"date-time":"2024-09-12T00:00:00Z","timestamp":1726099200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004564","name":"Ministry of Science and Technological Development, Republic of Serbia","doi-asserted-by":"publisher","award":["451-03-68\/2020\/14\/200156"],"award-info":[{"award-number":["451-03-68\/2020\/14\/200156"]}],"id":[{"id":"10.13039\/501100004564","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we introduce several new types of partial fractional derivatives in the continuous setting and the discrete setting. We analyze some classes of the abstract fractional differential equations and the abstract fractional difference equations depending on several variables, providing a great number of structural results, useful remarks and illustrative examples. Concerning some specific applications, we would like to mention here our investigation of the fractional partial differential inclusions with Riemann\u2013Liouville and Caputo derivatives. We also establish the complex characterization theorem for the multidimensional vector-valued Laplace transform and provide certain applications.<\/jats:p>","DOI":"10.3390\/axioms13090623","type":"journal-article","created":{"date-parts":[[2024,9,12]],"date-time":"2024-09-12T10:15:27Z","timestamp":1726136127000},"page":"623","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Multidimensional Fractional Calculus: Theory and Applications"],"prefix":"10.3390","volume":"13","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"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,9,12]]},"reference":[{"key":"ref_1","unstructured":"Bazhlekova, E. (2001). Fractional Evolution Equations in Banach Spaces. [Ph.D. Thesis, Eindhoven University of Technology]."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Diethelm, K. (2010). The Analysis of Fractional Differential Equations, Springer.","DOI":"10.1007\/978-3-642-14574-2"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Hilfer, R. (2000). Applications of Fractional Calculus in Physics, World Scientific.","DOI":"10.1142\/9789812817747"},{"key":"ref_4","unstructured":"Kilbas, A.A., Srivastava, H.M., and Trujillo, J.J. (2006). Theory and Applications of Fractional Differential Equations, Elsevier Science B.V."},{"key":"ref_5","unstructured":"Kosti\u0107, M. (2020). 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