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Certain fractional q-integrals and q-derivatives

  • R. P. Agarwal (a1)
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In a recent paper Al-Salam(1) has denned a fractional q-integral operator by the basic integral

(1) Where α ≠ 0, −1, −2, …. Using the series definition of the basic integrals, (1·1) is written as

valid for all α

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References
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(1)Al-Salam, W. A.Some fractional q-integrals and q-derivatives. Proc. Edinburgh Math. Soc. 15 (1966), 135140.
(2)Erdelyi, A.On some functional transformations. Univ. e Politecnico Torino Rend. Sem. Mat. 10 (1951), 217234.
(3)Hahn, W.Beiträge zur theorie der Heineschen Reihen Math. Nachr. 2 (1949), 340–79.
(4)Hahn, W.Über die höheren Heinschen reihen und eine einheitliche theorie der sogenannten speziellen funktionen. Math. Nachr. 3 (1950), 257294.
(5)Kober, H.On fractional integrals and derivatives. Quart. J. Math. Oxford Ser. 11 (1940), 193–21.
(6)Slater, L.J. Generalized Hypergeometric Functions. Cambridge University Press (1966).
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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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