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Operators of fractional integration

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Analytic Functions Kozubnik 1979

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 798))

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References

  1. BAKER, B.B. and COPSON, E.T.: The Mathematical Theory of Huygen's Principle, (Clarendon Press, Oxford 1950).

    MATH  Google Scholar 

  2. BORA, S.L. and SAXENA, R.K.: On fractional integration, Publ. Inst. Math., Beograd, 11 (25) (1971), 19–22.

    MathSciNet  MATH  Google Scholar 

  3. BRAAKSMA, B.L.J.: Asymptotic expansions and analytic continuations for a class of Barnes integrals, Comp. Mat. 15, (1963) 239–341.

    MathSciNet  MATH  Google Scholar 

  4. CHAKRABARTI, A.: On the solution of certain simultaneous pairs of dual integral equations, ZAMM 54 (1974), 383–387.

    Article  MathSciNet  MATH  Google Scholar 

  5. DOETSCH, G.: Theorie und Arwendung der Laplace Transformation (Springer-Verlag, Berlin 1937).

    Book  MATH  Google Scholar 

  6. ERDELYI, A.: On fractional integration and its applications to the theory of Hankel transforms, Quart. J. Math. Oxford 11 (1940), 293–303.

    Article  MathSciNet  MATH  Google Scholar 

  7. ERDELYI, A.: On some functional transformations, Univ. e Politec. Torino, Rend. Sem. Mat. 10 (1951), 217–234.

    MathSciNet  MATH  Google Scholar 

  8. ERDELYI, A.: An integral equation involving Legendre functions, SIAM J. Appl. Math. 12 (1964), 15–30.

    Article  MathSciNet  MATH  Google Scholar 

  9. ERDELYI, A., et al.: Tables of Integral Transforms, Vols. I and II (McGraw-Hill, New York 1954).

    Google Scholar 

  10. ERDELYI, A. and KOBER, H.: Some remarks on Hankel transforms, Quart. J. Math. Oxford 11 (1940), 212–221.

    Article  MathSciNet  MATH  Google Scholar 

  11. ERDELYI, A. and SNEDDON, I.N.: Fractional integration and dual integral equations, Can. J. Math. 14 (1962), 685–693.

    Article  MathSciNet  MATH  Google Scholar 

  12. FOX, C.: The G-and H-functions as symmetrical Fowrier kernels Trans. Amer. Math. Soc. 98 (1961), 395–429.

    MathSciNet  MATH  Google Scholar 

  13. FOX, C.: An inversion formula for the kernel K v (x), Proc. Cambridge Phil. Soc. 61 (1965), 457–467.

    Article  MATH  Google Scholar 

  14. GUPTA, K.C.: On the H-function, Annal. Soc. Sci. Bruxelles 79 (1965), 98–104.

    Google Scholar 

  15. HARDY, G.H. and LITTLEWOOD, J.E.: Some properties of fractional integrals, Math. Z. 27 (1928), 565–606.

    Article  MathSciNet  MATH  Google Scholar 

  16. INCE, E.L.: Ordinary Differential Equations (Dover Publ., New York 1956).

    MATH  Google Scholar 

  17. JAGETYA, R.N.: Solution of dual integral equations by fractional integration, Math. Edu., 4 (1970), 69–72; Triple integral equations and fractional integration, Univ. Nac. Tucumán Rev. Ser. A20 (1970), 41–47.

    MathSciNet  MATH  Google Scholar 

  18. KALLA, S.L.: Some theorems of fractional integration, Proc. Nat. Acad. Sci., India 36A (1966), 1007–1012.

    MathSciNet  MATH  Google Scholar 

  19. KALLA, S.L.: Some theorems of fractional integration-II, Proc. Nat. Acad. Sci., India 39A (1969), 49–56.

    MathSciNet  MATH  Google Scholar 

  20. KALLA, S.L. and SAXENA, R.K.: Integral operators involving hypergeometric functions, Math. Z. 108 (1969), 231–234.

    Article  MathSciNet  MATH  Google Scholar 

  21. KALLA, S.L. and SAXENA, R.K.: Integral operators involving hypergeometric functions-II, Univ. Nac. Tucumán, Rev. Ser. A24 (1974), 31–36.

    MathSciNet  MATH  Google Scholar 

  22. KALLA, S.L.: Fractional integration operators involving hypergeometric functions, Univ. Nac. Tucumán, Rev. Ser. A20 (1970) 93–100.

    MathSciNet  MATH  Google Scholar 

  23. KALLA, S.L.: Fractional integration operations involuing hypergeometric functions-II, Acta Mexicana Cie. Tecn. 3 (1969), 1–5

    MathSciNet  Google Scholar 

  24. KALLA, S.L.: Integral operators involving Fox's H-function, Acta Mexicana Cie. Tecn. 3 (1969), 117–122.

    MathSciNet  MATH  Google Scholar 

  25. KALLA, S.L.: Integral operators involving Fox's H-function-II, Acta Mexicana Cie. Tecn. (in press).

    Google Scholar 

  26. KALLA, S.L.: On operators of fractional integration, Mat. Notae 22 (1970), 89–93.

    MathSciNet  Google Scholar 

  27. KALLA, S.L.: On operators of fractional integration-II, Mat. Notae 26 (1976)

    Google Scholar 

  28. KALLA, S.L.: On the solution of an integral equation involving a kernel of Mellin-Barnes type integral, Kyungpook Math. J. 12 (1972), 93–101.

    MathSciNet  MATH  Google Scholar 

  29. KOBER, H.: On fractional integrals and derivatives, Quart. J. Math. Oxford 11 (1940), 193–211.

    Article  MathSciNet  MATH  Google Scholar 

  30. KOBER, H.: On a theorem of Schur and on fractional integrals of purely imaginary order, Trans. Amer. Math. Soc. 50 (1941), 160–174.

    MathSciNet  MATH  Google Scholar 

  31. LOVE, E.R.: Fractional derivatives of imaginary order, J. London Math. Soc. 3 (1971), 241–259.

    Article  MathSciNet  MATH  Google Scholar 

  32. LOVE, E.R. and YOUNG, L.C.: On fractional integration by parts, Proc. London Math. Soc. 44 (1938), 1–28.

    Article  MathSciNet  MATH  Google Scholar 

  33. LUKE, Y.L.: The Special Functions and Their Approximations, Vols. I & II (Academic Press, New York 1969).

    MATH  Google Scholar 

  34. MAKARENKO, L.G.: Certain triples of integral equations with Watson-type kernels, Ukrain. Math. J. 27 (1975–76), 564–567.

    Article  MATH  Google Scholar 

  35. MARTIC, B.: A note on fractional integration, Pub. Inst. Math. Beograd 16 (30), (1973), 111–113.

    MathSciNet  MATH  Google Scholar 

  36. MITTAL, P.K. and GUPTA, K.C.: An integral involving generalized functions of two variables, Proc. Indian Acad. Sci. A75 (1972), 117–123.

    MathSciNet  MATH  Google Scholar 

  37. MUNOT, P.C. and KALLA, S.L.: On an extension of generalized functions of two variables, Univ. Nac. Tucumán, Rev. Ser. A21 (1971), 67–84.

    MathSciNet  MATH  Google Scholar 

  38. RIESZ, M.: L'integrales de Riemann-Liouville et le probleme de Cauchy, Acta Math. 8 (1949), 1–123.

    Article  MathSciNet  MATH  Google Scholar 

  39. SAXENA, R.K.: On fractional integration operators, Math. Z. 96 (1967), 288–291.

    Article  MathSciNet  MATH  Google Scholar 

  40. SAXENA, R.K.: An inversion formula for the Varma trans form, Proc. Cambridge Phil. Soc. 62 (1966), 467–471.

    Article  MATH  Google Scholar 

  41. SAXENA, R.K. and SETHI, P.L.: On the formal solution of quadruole integral equations, Proc. Nat. Acad. Sci. India 42 (1972), 57–61.

    MathSciNet  MATH  Google Scholar 

  42. SNEDDON, I.N.: Mixed Boundary Value Problems in Potential Theory (North Holland Publishing Co., Amsterdam 1966).

    MATH  Google Scholar 

  43. SRIVASTAVA, H.M. and BUSCHMAN, R.G.: Composition of fractional integral operators involving Fox's H-function, Acta Mexicana Cie. Tecn. 7 (1973), 21–28.

    MathSciNet  MATH  Google Scholar 

  44. TITCHMARSH, E.C.: Introduction to the Theory of Fourier Integrals, 2nd Ed. (Clarendon Press, Oxford 1948).

    MATH  Google Scholar 

  45. VIRCHENKO, N.A. and MAKARENKO, L.G.: Some pairs of integral equations, Ukrain. Math. J. 27 (1975–76), 648–651.

    Article  MATH  Google Scholar 

  46. WIDDER, D.V.: The Laplace Transform (Princeton Univ. Press 1941).

    Google Scholar 

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  1. División de Postgrado, Facultad de Ingeniería, Universidad del Zulia, Maracaibo, Venezuela

    Shyam Lal Kalla

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  1. Shyam Lal Kalla
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Julian Ławrynowicz

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© 1980 Springer-Verlag

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Kalla, S.L. (1980). Operators of fractional integration. In: Ławrynowicz, J. (eds) Analytic Functions Kozubnik 1979. Lecture Notes in Mathematics, vol 798. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0097270

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  • DOI: https://doi.org/10.1007/BFb0097270

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  • Print ISBN: 978-3-540-09985-7

  • Online ISBN: 978-3-540-39247-7

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