{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,2]],"date-time":"2025-08-02T14:56:42Z","timestamp":1754146602656,"version":"3.41.2"},"reference-count":22,"publisher":"American Institute of Mathematical Sciences (AIMS)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["NHM"],"published-print":{"date-parts":[[2025]]},"DOI":"10.3934\/nhm.2025037","type":"journal-article","created":{"date-parts":[[2025,7,18]],"date-time":"2025-07-18T11:53:01Z","timestamp":1752839581000},"page":"868-884","source":"Crossref","is-referenced-by-count":0,"title":["Generalized fractional derivatives and fourier transforms in tempered distributions with applications"],"prefix":"10.3934","volume":"20","author":[{"given":"Amin Benaissa","family":"Cherif","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"name":"Department of Mathematics, Faculty of Mathematics and Informatics, University of Science and Technology of Oran Mohamed-Boudiaf (USTOMB), El Mnaouar, BP 1505, Bir El Djir, Oran 31000, Algeria","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fatima Zohra","family":"Ladrani","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dalal","family":"Alhwikem","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ahmed","family":"Hammoudi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Khaled","family":"Zennir","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Keltoum","family":"Bouhali","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"name":"Department of Exact Sciences, Oran Higher Training Teacher's School (ENSO), Oran, Algeria","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"name":"Department of Mathematics, College of science, Qassim University, Saudi Arabia","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"name":"Department of Mathematics and Informatics, Faculty of Science and Technology, University Ain Temouchent Belhadj Bouchaib, BP 284, Ain Temouchent 46000, Algeria","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"2321","reference":[{"key":"key-10.3934\/nhm.2025037-1","unstructured":"J. Machado, V. S. Kiryakova, F. Mainardi, A poster about the old history of fractional calculus, <i>Fract. Calc. Appl. Anal.<\/i>, <b>13<\/b> (2010), 447\u2013454. Available from: <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"http:\/\/hdl.handle.net\/10525\/1666\">http:\/\/hdl.handle.net\/10525\/1666<\/ext-link>."},{"key":"key-10.3934\/nhm.2025037-2","unstructured":"K. B. Oldham, J. Spanier, <i>The Fractional Calculus<\/i>, Academic Press, New York, 1974."},{"key":"key-10.3934\/nhm.2025037-3","unstructured":"S. G. Samko, A. A. Kilbas, O. I. Marichev, <i>Fractional Integrals and Derivatives<\/i>, translated from the 1987 Russian original, Gordon and Breach, Yverdon, 1993."},{"key":"key-10.3934\/nhm.2025037-4","doi-asserted-by":"crossref","unstructured":"M. D. Ortigueira, <i>Fractional Calculus for Scientists and Engineers<\/i>, Springer Science &amp; Business Media, Dordrecht, 2011.","DOI":"10.1007\/978-94-007-0747-4"},{"key":"key-10.3934\/nhm.2025037-5","doi-asserted-by":"publisher","unstructured":"T. Kaczorek, D. Idczak, Cauchy formula for the time-varying linear systems with Caputo derivative, <i>Fract. Calc. Appl. Anal.<\/i>, <b>20<\/b> (2017), 494\u2013505. https:\/\/doi.org\/10.1515\/fca-2017-0025","DOI":"10.1515\/fca-2017-0025"},{"key":"key-10.3934\/nhm.2025037-6","doi-asserted-by":"publisher","unstructured":"D. Idczak, Riemann\u2013Liouville derivatives of abstract functions and Sobolev spaces, <i>Fract. Calc. Appl. Anal.<\/i>, <b>25<\/b> (2022), 1260\u20131293. https:\/\/doi.org\/10.1007\/s13540-022-00058-8","DOI":"10.1007\/s13540-022-00058-8"},{"key":"key-10.3934\/nhm.2025037-7","doi-asserted-by":"publisher","unstructured":"M. Caputo, M. Fabrizio, A new definition of fractional derivative without singular kernel, <i>Progr. Fract. Diff. Appl.<\/i>, <b>1<\/b> (2015), 73\u201385. http:\/\/dx.doi.org\/10.12785\/pfda\/010201","DOI":"10.12785\/pfda\/010201"},{"key":"key-10.3934\/nhm.2025037-8","doi-asserted-by":"publisher","unstructured":"A. Atangana, D. Baleanu, New fractional derivatives with nonlocal and nonsingular kernel: Theory and application to heat transfer model, <i>Thermal Sci.<\/i>, <b>20<\/b> (2016), 763\u2013769. https:\/\/doi.org\/10.2298\/TSCI160111018A","DOI":"10.2298\/TSCI160111018A"},{"key":"key-10.3934\/nhm.2025037-9","doi-asserted-by":"crossref","unstructured":"C. A. Monje, Y. Chen, B. M. Vinagre, D. Xue, V. Feliu, <i>Fractional-Order Systems and Controls: Fundamentals and Applications<\/i>, London: Springer London, 2010.","DOI":"10.1007\/978-1-84996-335-0"},{"key":"key-10.3934\/nhm.2025037-10","unstructured":"J. Dziuba\u0144ski, M. Preisner, Tempered fractional calculus and applications to harmonic analysis, <i>J. Funct. Anal.<\/i>, <b>270<\/b> (2016), 3747\u20133776."},{"key":"key-10.3934\/nhm.2025037-11","unstructured":"S. Albeverio, R. H\u00f8egh-Krohn, Fractional powers of self-adjoint operators and tempered distributions, <i>Potential Anal.<\/i>, <b>26<\/b> (2007), 33\u201352."},{"key":"key-10.3934\/nhm.2025037-12","unstructured":"G. H\u00f6rmann, M. Oberguggenberger, Microlocal analysis of tempered distributions with applications, <i>J. Fourier Anal. Appl.<\/i>, <b>13<\/b> (2007), 563\u2013594."},{"key":"key-10.3934\/nhm.2025037-13","unstructured":"M. W. Wong, <i>Introduction to Pseudo-Differential Operators<\/i>, World Scientific Publishing Company, 2014."},{"key":"key-10.3934\/nhm.2025037-14","doi-asserted-by":"publisher","unstructured":"R. S. Pathak, Akhilesh Prasad, Manish Kumar, Fractional Fourier transform of tempered distributions and generalized pseudo-differential operator, <i>J. Pseudo-Differ. Oper. Appl.<\/i>, <b>3<\/b> (2012), 239\u2013254. https:\/\/doi.org\/10.1007\/s11868-012-0047-8","DOI":"10.1007\/s11868-012-0047-8"},{"key":"key-10.3934\/nhm.2025037-15","doi-asserted-by":"crossref","unstructured":"D. M. Ashwini, D. K. Kishor, A. Fernandez, H. M. Fahad, On tempered fractional calculus with respect to functions and the associated fractional differential equations, <i>Math. Meth. Appl. Sci.<\/i>, <b>45<\/b>, (2022), 11134\u201311157. <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/doi.org\/10.1002\/mma.8441\">https:\/\/doi.org\/10.1002\/mma.8441<\/ext-link>","DOI":"10.1002\/mma.8441"},{"key":"key-10.3934\/nhm.2025037-16","unstructured":"R. A. Adams, J. J. F. Fournier, <i>Pure and Applied Mathematics<\/i>, Elsevier\/Academic Press, Amsterdam, 2003."},{"key":"key-10.3934\/nhm.2025037-17","unstructured":"H. Brezis, <i>Functional Analysis, Sobolev Spaces and Partial Differential Equations<\/i>, Universitext, 1st edition, Springer, New York, 2011. <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/doi.org\/10.1007\/978-0-387-70914-7\">https:\/\/doi.org\/10.1007\/978-0-387-70914-7<\/ext-link>"},{"key":"key-10.3934\/nhm.2025037-18","unstructured":"R. Picard, <i>Hilbert Space Approach to Some Classical Transforms<\/i>, Pitman Research Notes in Mathematics Series, Harlow and New York: Longman Scientific &amp; Technical and Wiley, 1989."},{"key":"key-10.3934\/nhm.2025037-19","doi-asserted-by":"publisher","unstructured":"R. Picard, S. Trostorff, M. Waurick, On evolutionary equations with material laws containing fractional integrals, <i>Math. Methods Appl. Sci.<\/i>, <b>38<\/b> (2015), 3141\u20133154. https:\/\/doi.org\/10.1002\/mma.3286","DOI":"10.1002\/mma.3286"},{"key":"key-10.3934\/nhm.2025037-20","doi-asserted-by":"publisher","unstructured":"K. Diethelm, K. Kitzing, R. Picard, S. Siegmund, S. Trostorff, M. Waurick, A hilbert space approach to fractional differential equations, <i>J. Dyn. Diff. Equat.<\/i>, <b>34<\/b> (2022), 481\u2013504. https:\/\/doi.org\/10.1007\/s10884-020-09932-6","DOI":"10.1007\/s10884-020-09932-6"},{"key":"key-10.3934\/nhm.2025037-21","doi-asserted-by":"publisher","unstructured":"R. Zacher, Weak solutions of abstract evolutionary integro-differential equations in Hilbert spaces, <i>Funkcial. Ekvac.<\/i>, <b>52<\/b> (2009), 1\u201318. https:\/\/doi.org\/10.1619\/fesi.52.1","DOI":"10.1619\/fesi.52.1"},{"key":"key-10.3934\/nhm.2025037-22","doi-asserted-by":"publisher","unstructured":"R. Gorenflo, Y. Luchko, M. Yamamoto, Time-fractional diffusion equation in the fractional Sobolev spaces, <i>Fract. Calc. Appl. Anal.<\/i>, <b>18<\/b> (2015), 799\u2013820. https:\/\/doi.org\/10.1515\/fca-2015-0048","DOI":"10.1515\/fca-2015-0048"}],"container-title":["Networks and Heterogeneous Media"],"original-title":[],"link":[{"URL":"http:\/\/www.aimspress.com\/article\/doi\/10.3934\/nhm.2025037?viewType=html","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,18]],"date-time":"2025-07-18T11:53:05Z","timestamp":1752839585000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.aimspress.com\/article\/doi\/10.3934\/nhm.2025037"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025]]},"references-count":22,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2025]]}},"URL":"https:\/\/doi.org\/10.3934\/nhm.2025037","relation":{},"ISSN":["1556-1801"],"issn-type":[{"value":"1556-1801","type":"print"}],"subject":[],"published":{"date-parts":[[2025]]}}}