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picture1_Derivatives Calculus Pdf 172176 | Foundationsoffractionalcalculus Sanjakonjik


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File: Derivatives Calculus Pdf 172176 | Foundationsoffractionalcalculus Sanjakonjik
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 ...

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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
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        Sanja Konjik (Uni Novi Sad)              Foundations of fractional calculus          Novi Sad, Feb 6-8, 2015      3 / 22        Close
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...Foundations of fractional calculus sanja konjik department mathematics and informatics university novi sad serbia winter school on non standard forms teaching physics experimental modeling approach february uni feb derivatives integrals f x z lim dx y b a modern was founded in the th century by isaac newton gottfried leibniz zab born n fd dtn what if order will be it lead to paradox from which one day useful consequences start drawn jj ii g de l hopital w j i back...

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