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An algebraic definition of fractional differentiation

Part of the Lecture Notes in Mathematics book series (LNM,volume 457)

Abstract

Suppose I is an open real interval, and V a subspace of C(I) invariant under D, differentiation. It is shown that if V contains a polynomial of positive degree, then D has no homogeneous qth root on V, for any integer q > 1. This conclusion is not generally true if I is replaced by an arbitrary open set in the reals. Necessary and sufficient conditions for the existence of qth roots of D on finite dimensional subspaces of C(I) invariant under D, in terms of the differential equations of which such subspaces are the solution spaces, are obtained.

Keywords

  • Characteristic Polynomial
  • Open Interval
  • Real Vector Space
  • Complex Vector Space
  • Positive Degree

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Agnew, R. P., Differential Equations, New York; McGraw-Hill 1942.

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© 1975 Springer-Verlag

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Johnson, P.D. (1975). An algebraic definition of fractional differentiation. In: Ross, B. (eds) Fractional Calculus and Its Applications. Lecture Notes in Mathematics, vol 457. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0067107

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  • DOI: https://doi.org/10.1007/BFb0067107

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07161-7

  • Online ISBN: 978-3-540-69975-0

  • eBook Packages: Springer Book Archive