{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T23:16:38Z","timestamp":1775603798783,"version":"3.50.1"},"reference-count":18,"publisher":"Walter de Gruyter GmbH","issue":"1","license":[{"start":{"date-parts":[[2016,1,1]],"date-time":"2016-01-01T00:00:00Z","timestamp":1451606400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/3.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016,1,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>In this short note we present a new general definition of local fractional derivative, that depends on an unknown kernel. For some appropriate choices of the kernel we obtain some known cases. We establish a relation between this new concept and ordinary differentiation. Using such formula, most of the fundamental properties of the fractional derivative can be derived directly.<\/jats:p>","DOI":"10.1515\/math-2016-0104","type":"journal-article","created":{"date-parts":[[2017,1,5]],"date-time":"2017-01-05T10:06:48Z","timestamp":1483610808000},"page":"1122-1124","source":"Crossref","is-referenced-by-count":54,"title":["A remark on local fractional calculus and ordinary derivatives"],"prefix":"10.1515","volume":"14","author":[{"given":"Ricardo","family":"Almeida","sequence":"first","affiliation":[{"name":"Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal"}]},{"given":"Ma\u0142gorzata","family":"Guzowska","sequence":"additional","affiliation":[{"name":"Faculty of Economics and Management, University of Szczecin, 71-101 Szczecin, Poland"}]},{"given":"Tatiana","family":"Odzijewicz","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Mathematical Economics, Warsaw School of Economics, 02-554 Warsaw, Poland"}]}],"member":"374","published-online":{"date-parts":[[2016,12,31]]},"reference":[{"key":"2022042708053912124_j_math-2016-0104_ref_001_w2aab3b8e1190b1b7b1ab2b1b1Aa","unstructured":"Abdeljawad T., On conformable fractional calulus, preprint."},{"key":"2022042708053912124_j_math-2016-0104_ref_002_w2aab3b8e1190b1b7b1ab2b1b2Aa","doi-asserted-by":"crossref","unstructured":"Anderson D.R., Avery R.I., Fractional-order boundary value problem with Sturm-Liouville boundary conditions, Electron. J. Differ. Equ., Volume 2015, 29, 1-10, 2015.","DOI":"10.1186\/s13662-015-0413-y"},{"key":"2022042708053912124_j_math-2016-0104_ref_003_w2aab3b8e1190b1b7b1ab2b1b3Aa","doi-asserted-by":"crossref","unstructured":"Anderson D.R., Ulness D.J., Properties of the Katugampola fractional derivative with potential application in quantum mechanics, J. Math. Phys 56, 063502, 2015.","DOI":"10.1063\/1.4922018"},{"key":"2022042708053912124_j_math-2016-0104_ref_004_w2aab3b8e1190b1b7b1ab2b1b4Aa","doi-asserted-by":"crossref","unstructured":"Atangana A., Goufo E.F.D., Extension of Matched Asymptotic Method to Fractional Boundary Layers Problems, Mathematical Problems in Engineering, Volume 2014, 107535, 7 pages.","DOI":"10.1155\/2014\/107535"},{"key":"2022042708053912124_j_math-2016-0104_ref_005_w2aab3b8e1190b1b7b1ab2b1b5Aa","doi-asserted-by":"crossref","unstructured":"Atangana A., Noutchie S.C.O., Model of Break-Bone Fever via Beta-Derivatives, BioMed Research International, Volume 2014, 523159, 10 pages.","DOI":"10.1155\/2014\/523159"},{"key":"2022042708053912124_j_math-2016-0104_ref_006_w2aab3b8e1190b1b7b1ab2b1b6Aa","doi-asserted-by":"crossref","unstructured":"Babakhani A., Daftardar-Gejji V, On calculus of local fractional derivatives, J. Math. Anal. Appl. 270 (1), 66-79, 2002.","DOI":"10.1016\/S0022-247X(02)00048-3"},{"key":"2022042708053912124_j_math-2016-0104_ref_007_w2aab3b8e1190b1b7b1ab2b1b7Aa","doi-asserted-by":"crossref","unstructured":"Batarfi H., Losada J., Nieto J.J., Shammakh W., Three-point boundary value problems for conformable fractional differential equations, Journal of function spaces, Volume 2015, 706383, 6 pages.","DOI":"10.1155\/2015\/706383"},{"key":"2022042708053912124_j_math-2016-0104_ref_008_w2aab3b8e1190b1b7b1ab2b1b8Aa","unstructured":"\u00c7enesiz Y, Kurt A., The solution of time fractional heat equation with new fractional derivative definition, in Recent Advances in Applied Mathematics, Modelling and Simulation (eds N.E. Mastorakis, M. Demiralp, N. Mukhopadhyay and F. Mainardi) North Atlantic University Union, 195-198, 2014."},{"key":"2022042708053912124_j_math-2016-0104_ref_009_w2aab3b8e1190b1b7b1ab2b1b9Aa","doi-asserted-by":"crossref","unstructured":"Chen Y, Yan Y, Zhang K., On the local fractional derivative, J. Math. Anal. Appl. 362 (1), 17-33, 2010.","DOI":"10.1016\/j.jmaa.2009.08.014"},{"key":"2022042708053912124_j_math-2016-0104_ref_010_w2aab3b8e1190b1b7b1ab2b1c10Aa","doi-asserted-by":"crossref","unstructured":"Abu Hammad M., Khalil R., Legendre fractional differential equation and Legender fractional polynomials, Int. J. Appl. Math. Res. 3(3), 214-219, 2014.","DOI":"10.14419\/ijamr.v3i3.2747"},{"key":"2022042708053912124_j_math-2016-0104_ref_011_w2aab3b8e1190b1b7b1ab2b1c11Aa","unstructured":"Hesameddini E., Asadollahifard E., Numerical solution of multi-order fractional differential equations via the sinc collocation method, Iran. J. Numer. Anal. Optim. 5 (1), 37-48, 2015."},{"key":"2022042708053912124_j_math-2016-0104_ref_012_w2aab3b8e1190b1b7b1ab2b1c12Aa","unstructured":"Katumgapola U., A new fractional derivative with classical properties, preprint."},{"key":"2022042708053912124_j_math-2016-0104_ref_013_w2aab3b8e1190b1b7b1ab2b1c13Aa","doi-asserted-by":"crossref","unstructured":"Khalil R., Al Horani M., Yousef A., Sababheh M., A new definition of fractional derivative, J. Comput. Appl. Math. 264. 65-70, 2014.","DOI":"10.1016\/j.cam.2014.01.002"},{"key":"2022042708053912124_j_math-2016-0104_ref_014_w2aab3b8e1190b1b7b1ab2b1c14Aa","unstructured":"Kilbas A.A., Srivastava H.M., Trujillo J.J., Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies, 204. Elsevier Science B.V., Amsterdam, 2006."},{"key":"2022042708053912124_j_math-2016-0104_ref_015_w2aab3b8e1190b1b7b1ab2b1c15Aa","doi-asserted-by":"crossref","unstructured":"Kolwankar K.M., Gangal A.D., Fractional differentiability of nowhere differentiable functions and dimension, Chaos 6, 505-513, 1996.","DOI":"10.1063\/1.166197"},{"key":"2022042708053912124_j_math-2016-0104_ref_016_w2aab3b8e1190b1b7b1ab2b1c16Aa","doi-asserted-by":"crossref","unstructured":"Kolwankar K.M., Gangal A.D., H\u00f6lder exponents of irregular signals and local fractional derivatives, Pramana J. Phys. 48, 49-68, 1997.","DOI":"10.1007\/BF02845622"},{"key":"2022042708053912124_j_math-2016-0104_ref_017_w2aab3b8e1190b1b7b1ab2b1c17Aa","unstructured":"Podlubny I., Fractional differential equations, Mathematics in Science and Engineering, 198. Academic Press, Inc., San Diego, CA, 1999."},{"key":"2022042708053912124_j_math-2016-0104_ref_018_w2aab3b8e1190b1b7b1ab2b1c18Aa","unstructured":"\u00dcnal E., G\u01d2kdogan A., \u00c7elik E., Solutions around a regular \u03b1 singular point of a sequential conformable fractional differential equation, preprint."}],"container-title":["Open Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/math\/14\/1\/article-p1122.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/math-2016-0104\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/math-2016-0104\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,4,27]],"date-time":"2022-04-27T11:15:08Z","timestamp":1651058108000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/math-2016-0104\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,1,1]]},"references-count":18,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2016,6,9]]},"published-print":{"date-parts":[[2016,1,1]]}},"alternative-id":["10.1515\/math-2016-0104"],"URL":"https:\/\/doi.org\/10.1515\/math-2016-0104","relation":{},"ISSN":["2391-5455"],"issn-type":[{"value":"2391-5455","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,1,1]]}}}