Человек, опередивший время

211 Âîñïîìèíàíèÿ äðóçåé è ñîðàòíèêîâ SOME PIONEERS OF THE APPLICATIONS OF FRACTIONAL CALCULUS* Duarte Valerio, Jose Tenreiro Machado, Virginia Kiryakova Abstract. In the last decades fractional calculus (FC) became an area of intensive research and development. This paper goes back and recalls important pioneers that started to apply FC to scientific and engineering problems during the nineteenth and twentieth centuries. Those we present are, in alphabetical order: Niels Abel, Kenneth and Robert Cole, Andrew Gemant, Andrey N. Gerasimov, Oliver Heaviside, Paul Levy, Rashid Sh. Nigmatullin, Yuri N. Rabotnov, George Scott Blair. Keywords and Phrases : fract ional calculus, applications, pioneers, Abel, Cole, Gemant, Gerasimov, Heaviside, Levy, Nigmatullin, Rabotnov, Scott Blair Introduction In 1695 Gottfried Leibniz asked Guillaume l’Hopital if the (integer) order of derivatives and integrals could be extended. Was it possible if the order was some irrational, fractional or complex number? «Dream commands l i fe» and thi s idea mot i va t ed many mathematicians, physicists and engineers to develop the concept of fractional calculus (FC). During four centuries many famous mathematicians contributed to the theo- retical development of FC. We can list (in alphabetical order) some important researchers since 1695 (see posters at http://www.math.bas.bg/~fcaa) : *Ñòàòüÿ «Ïèîíåðû ïðèëîæå- íèé äðîáíîãî ìàòåìàòè÷åñêîãî àíà- ëèçà» îïóáëèêîâàííà â 2014 ã. àâòîðèòåòíûì æóðíàëîì Fractional Calculus and Applied Analysis î Ð.Ø. Íèãìàòóëëèíå, âïåðâûå íà àïïàðàòíîì óðîâíå ðåàëèçîâàâøåì îïåðàöèþ äðîáíîãî äèôôåðåíöè- ðîâàíèÿ äëÿ îáðàáîòêè ñèãíàëîâ. Íàó÷íûå ðàçðàáîòêè