Fernandez, ArranBaleanu, Dumitru02.02. Matematik02. Fen-Edebiyat Fakültesi01. Çankaya Üniversitesi2019-12-252025-09-182019-12-252025-09-182019Baleanu, Dumitru; Fernandez, Arran, "On Fractional Operators and Their Classifications", Mathematics, Vol. 7, No. 9, (September 2019).2227-7390https://doi.org/10.3390/math7090830https://hdl.handle.net/20.500.12416/14915Fernandez, Arran/0000-0002-1491-1820Fractional calculus dates its inception to a correspondence between Leibniz and L'Hopital in 1695, when Leibniz described "paradoxes" and predicted that "one day useful consequences will be drawn" from them. In today's world, the study of non-integer orders of differentiation has become a thriving field of research, not only in mathematics but also in other parts of science such as physics, biology, and engineering: many of the "useful consequences" predicted by Leibniz have been discovered. However, the field has grown so far that researchers cannot yet agree on what a "fractional derivative" can be. In this manuscript, we suggest and justify the idea of classification of fractional calculus into distinct classes of operators.eninfo:eu-repo/semantics/openAccessIntegral TransformsConvergent SeriesFractional CalculusArticle10.3390/math70908302-s2.0-85072337052