Advertisement

Operators of fractional integration

  • Shyam Lal Kalla
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 798)

Keywords

Integral Equation Integral Operator Fractional Integration Fractional Integration Operator Dual Integral Equation 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    BAKER, B.B. and COPSON, E.T.: The Mathematical Theory of Huygen's Principle, (Clarendon Press, Oxford 1950).zbMATHGoogle Scholar
  2. [2]
    BORA, S.L. and SAXENA, R.K.: On fractional integration, Publ. Inst. Math., Beograd, 11 (25) (1971), 19–22.MathSciNetzbMATHGoogle Scholar
  3. [3]
    BRAAKSMA, B.L.J.: Asymptotic expansions and analytic continuations for a class of Barnes integrals, Comp. Mat. 15, (1963) 239–341.MathSciNetzbMATHGoogle Scholar
  4. [4]
    CHAKRABARTI, A.: On the solution of certain simultaneous pairs of dual integral equations, ZAMM 54 (1974), 383–387.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    DOETSCH, G.: Theorie und Arwendung der Laplace Transformation (Springer-Verlag, Berlin 1937).CrossRefzbMATHGoogle Scholar
  6. [6]
    ERDELYI, A.: On fractional integration and its applications to the theory of Hankel transforms, Quart. J. Math. Oxford 11 (1940), 293–303.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    ERDELYI, A.: On some functional transformations, Univ. e Politec. Torino, Rend. Sem. Mat. 10 (1951), 217–234.MathSciNetzbMATHGoogle Scholar
  8. [8]
    ERDELYI, A.: An integral equation involving Legendre functions, SIAM J. Appl. Math. 12 (1964), 15–30.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    ERDELYI, A., et al.: Tables of Integral Transforms, Vols. I and II (McGraw-Hill, New York 1954).Google Scholar
  10. [10]
    ERDELYI, A. and KOBER, H.: Some remarks on Hankel transforms, Quart. J. Math. Oxford 11 (1940), 212–221.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    ERDELYI, A. and SNEDDON, I.N.: Fractional integration and dual integral equations, Can. J. Math. 14 (1962), 685–693.MathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    FOX, C.: The G-and H-functions as symmetrical Fowrier kernels Trans. Amer. Math. Soc. 98 (1961), 395–429.MathSciNetzbMATHGoogle Scholar
  13. [13]
    FOX, C.: An inversion formula for the kernel K v (x), Proc. Cambridge Phil. Soc. 61 (1965), 457–467.CrossRefzbMATHGoogle Scholar
  14. [14]
    GUPTA, K.C.: On the H-function, Annal. Soc. Sci. Bruxelles 79 (1965), 98–104.Google Scholar
  15. [15]
    HARDY, G.H. and LITTLEWOOD, J.E.: Some properties of fractional integrals, Math. Z. 27 (1928), 565–606.MathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    INCE, E.L.: Ordinary Differential Equations (Dover Publ., New York 1956).zbMATHGoogle Scholar
  17. [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.MathSciNetzbMATHGoogle Scholar
  18. [18]
    KALLA, S.L.: Some theorems of fractional integration, Proc. Nat. Acad. Sci., India 36A (1966), 1007–1012.MathSciNetzbMATHGoogle Scholar
  19. [19]
    KALLA, S.L.: Some theorems of fractional integration-II, Proc. Nat. Acad. Sci., India 39A (1969), 49–56.MathSciNetzbMATHGoogle Scholar
  20. [20]
    KALLA, S.L. and SAXENA, R.K.: Integral operators involving hypergeometric functions, Math. Z. 108 (1969), 231–234.MathSciNetCrossRefzbMATHGoogle Scholar
  21. [21]
    KALLA, S.L. and SAXENA, R.K.: Integral operators involving hypergeometric functions-II, Univ. Nac. Tucumán, Rev. Ser. A24 (1974), 31–36.MathSciNetzbMATHGoogle Scholar
  22. [22]
    KALLA, S.L.: Fractional integration operators involving hypergeometric functions, Univ. Nac. Tucumán, Rev. Ser. A20 (1970) 93–100.MathSciNetzbMATHGoogle Scholar
  23. [23]
    KALLA, S.L.: Fractional integration operations involuing hypergeometric functions-II, Acta Mexicana Cie. Tecn. 3 (1969), 1–5MathSciNetGoogle Scholar
  24. [24]
    KALLA, S.L.: Integral operators involving Fox's H-function, Acta Mexicana Cie. Tecn. 3 (1969), 117–122.MathSciNetzbMATHGoogle Scholar
  25. [25]
    KALLA, S.L.: Integral operators involving Fox's H-function-II, Acta Mexicana Cie. Tecn. (in press).Google Scholar
  26. [26]
    KALLA, S.L.: On operators of fractional integration, Mat. Notae 22 (1970), 89–93.MathSciNetGoogle Scholar
  27. [27]
    KALLA, S.L.: On operators of fractional integration-II, Mat. Notae 26 (1976)Google Scholar
  28. [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.MathSciNetzbMATHGoogle Scholar
  29. [29]
    KOBER, H.: On fractional integrals and derivatives, Quart. J. Math. Oxford 11 (1940), 193–211.MathSciNetCrossRefzbMATHGoogle Scholar
  30. [30]
    KOBER, H.: On a theorem of Schur and on fractional integrals of purely imaginary order, Trans. Amer. Math. Soc. 50 (1941), 160–174.MathSciNetzbMATHGoogle Scholar
  31. [31]
    LOVE, E.R.: Fractional derivatives of imaginary order, J. London Math. Soc. 3 (1971), 241–259.MathSciNetCrossRefzbMATHGoogle Scholar
  32. [32]
    LOVE, E.R. and YOUNG, L.C.: On fractional integration by parts, Proc. London Math. Soc. 44 (1938), 1–28.MathSciNetCrossRefzbMATHGoogle Scholar
  33. [33]
    LUKE, Y.L.: The Special Functions and Their Approximations, Vols. I & II (Academic Press, New York 1969).zbMATHGoogle Scholar
  34. [34]
    MAKARENKO, L.G.: Certain triples of integral equations with Watson-type kernels, Ukrain. Math. J. 27 (1975–76), 564–567.CrossRefzbMATHGoogle Scholar
  35. [35]
    MARTIC, B.: A note on fractional integration, Pub. Inst. Math. Beograd 16 (30), (1973), 111–113.MathSciNetzbMATHGoogle Scholar
  36. [36]
    MITTAL, P.K. and GUPTA, K.C.: An integral involving generalized functions of two variables, Proc. Indian Acad. Sci. A75 (1972), 117–123.MathSciNetzbMATHGoogle Scholar
  37. [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.MathSciNetzbMATHGoogle Scholar
  38. [38]
    RIESZ, M.: L'integrales de Riemann-Liouville et le probleme de Cauchy, Acta Math. 8 (1949), 1–123.MathSciNetCrossRefzbMATHGoogle Scholar
  39. [39]
    SAXENA, R.K.: On fractional integration operators, Math. Z. 96 (1967), 288–291.MathSciNetCrossRefzbMATHGoogle Scholar
  40. [40]
    SAXENA, R.K.: An inversion formula for the Varma trans form, Proc. Cambridge Phil. Soc. 62 (1966), 467–471.CrossRefzbMATHGoogle Scholar
  41. [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.MathSciNetzbMATHGoogle Scholar
  42. [42]
    SNEDDON, I.N.: Mixed Boundary Value Problems in Potential Theory (North Holland Publishing Co., Amsterdam 1966).zbMATHGoogle Scholar
  43. [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.MathSciNetzbMATHGoogle Scholar
  44. [44]
    TITCHMARSH, E.C.: Introduction to the Theory of Fourier Integrals, 2nd Ed. (Clarendon Press, Oxford 1948).zbMATHGoogle Scholar
  45. [45]
    VIRCHENKO, N.A. and MAKARENKO, L.G.: Some pairs of integral equations, Ukrain. Math. J. 27 (1975–76), 648–651.CrossRefzbMATHGoogle Scholar
  46. [46]
    WIDDER, D.V.: The Laplace Transform (Princeton Univ. Press 1941).Google Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • Shyam Lal Kalla
    • 1
  1. 1.División de Postgrado, Facultad de IngenieríaUniversidad del ZuliaMaracaiboVenezuela

Personalised recommendations