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Foundations of fractional calculus Sanja Konjik Department of Mathematics and Informatics, University of Novi Sad, Serbia Winter School on Non-Standard Forms of Teaching Mathematics and Physics: Experimental and Modeling Approach Novi Sad, February 6-8, 2015 Sanja Konjik (Uni Novi Sad) Foundations of fractional calculus Novi Sad, Feb 6-8, 2015 1 / 22 derivatives integrals f (x +∆x)−f(x ) Z f ′(x ) = lim 0 0 F(x) = f (x)dx ⇒ F′(x)=f(x) 0 ∆x→0 ∆x y Z b f(x)dx a a b x Calculus Modern calculus was founded in the 17th century by Isaac Newton and Gottfried Leibniz. Sanja Konjik (Uni Novi Sad) Foundations of fractional calculus Novi Sad, Feb 6-8, 2015 2 / 22 Calculus Modern calculus was founded in the 17th century by Isaac Newton and Gottfried Leibniz. derivatives integrals f (x +∆x)−f(x ) Z f ′(x ) = lim 0 0 F(x) = f (x)dx ⇒ F′(x)=f(x) 0 ∆x→0 ∆x y Zab f(x)dx a b x Sanja Konjik (Uni Novi Sad) Foundations of fractional calculus Novi Sad, Feb 6-8, 2015 2 / 22 Fractional Calculus was born in 1695 n fd dtn What if the order will be n = ½? It will lead to a paradox, from which one day useful consequences will be Start drawn. JJ II G.F.A. de L’Hôpital G.W. Leibniz J I 10 / 90 (1661–1704) (1646–1716) Back Full screen Sanja Konjik (Uni Novi Sad) Foundations of fractional calculus Novi Sad, Feb 6-8, 2015 3 / 22 Close End
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