Pacific Journal of Mathematics

A fractional Leibniz $q$-formula.

W. A. Al-Salam and A. Verma

Article information

Source
Pacific J. Math., Volume 60, Number 2 (1975), 1-9.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102868429

Mathematical Reviews number (MathSciNet)
MR0404546

Zentralblatt MATH identifier
0328.44005

Subjects
Primary: 26A33: Fractional derivatives and integrals

Citation

Al-Salam, W. A.; Verma, A. A fractional Leibniz $q$-formula. Pacific J. Math. 60 (1975), no. 2, 1--9. https://projecteuclid.org/euclid.pjm/1102868429


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References

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  • [2] W. A. Al-Salam, Some fractional q-integrals and g-derivatives, Proc. Edinburgh Math. Soc, 15 (1966), 135-140.
  • [3] H. T. Davis, The application of fractional operators to functional equations, American J. of Mathematics, 49 (1927), 123-142.
  • [4] W. Hahn, LJber orthogonale Polynome, die q-Differenzengleichungen geniigen, Mathematische Nachrichten, 2 (1949), 4-34.
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  • [6] F. H. Jackson, q-Form of Taylor's theorem, Messenger of Mathematics, 39 (1909), 62-64.
  • [7] J. Liouville, Sur le calcul des differencelies a indices quelconques, Journale de Ecole Polytechni- que Ser. 1, 21 (1832), 71-161.
  • [8] T. J. Osier, Leibniz rule for fractional derivatives generalized and application to infinite series, SIAM J. Appl. Math., 18 (1970), 658-674.
  • [9] Y. Watanabe, Notes on the generalized derivative of Riemann-Liouville and its application to Leibniz formula, Tohoku Math. J., 34 (1931), 8-41.