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Generalized Differential and Integral Operators

  • Trifce Sandev
  • Živorad Tomovski
Chapter
First Online:
Part of the Developments in Mathematics book series (DEVM, volume 61)

Abstract

From the time of discovery of calculus by Leibniz, he studied the problem of fractional differentiations. 30 September 1695, the day when Leibniz sent a letter to L’Hôpital with a reply of the L’Hôpital’s question related to the differentiation of a function of order n = 1∕2, became a birthday of the fractional calculus. By using the Leibniz product rule and the binomial theorem he obtained some paradoxical results. Euler partially resolved the Leibniz paradox by introducing the gamma function as 1 ⋅ 2 ⋅… ⋅ n = n! = Γ(n + 1). Therefore, the fractional calculus has attracted attention to a range of celebrated mathematicians and physicists, such as Leibniz, Euler, Laplace, Lacroix, Fourier, Abel, Liouville, Riemann, Grünwald, Letnikov, to name but a few.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Trifce Sandev
    • 1
  • Živorad Tomovski
    • 2
  1. 1.Research Center for Computer Science and Information TechnologiesMacedonian Academy of Sciences and ArtsSkopjeNorth Macedonia
  2. 2.Faculty of Natural Sciences and Mathematics, Institute of MathematicsSs. Cyril and Methodius University in SkopjeSkopjeNorth Macedonia

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