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Certain Fractional Integrals and Image Formulas Of Generalized $\mathtt{k}$-Bessel Function

Praveen Agarwal|최준상|Mehar Chand|Gurmej Singh
대한수학회 (The Korean Mathematical Society)|2018.04|대한수학회논문집 (Communications of the KMS)|제33권 제2호|pp. 423-436

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참고문헌

키워드

Laplace transformFox-Wright function$\mathtt{k}$-Pochhammer symbol$\mathtt{k}$-gamma functiongeneralized $\mathtt{k}$-Bessel functionbeta transformWhittaker transformSaigo hypergeometric fractional integral operators
주제분류수학

초록

We aim to establish certain Saigo hypergeometric fractional integral formulas for a finite product of the generalized $\mathtt{k}$-Bessel functions, which are also used to present image formulas of several integral transforms including beta transform, Laplace transform, and Whittaker transform. The results presented here are potentially useful, and, being very general, can yield a large number of special cases, only two of which are explicitly demonstrated.

Abstract

We aim to establish certain Saigo hypergeometric fractional integral formulas for a finite product of the generalized $\mathtt{k}$-Bessel functions, which are also used to present image formulas of several integral transforms including beta transform, Laplace transform, and Whittaker transform. The results presented here are potentially useful, and, being very general, can yield a large number of special cases, only two of which are explicitly demonstrated.

참고문헌 (16)

  1. P. Agarwal, "Certain fractional kinetic equations involving the product of generalized k-Bessel function", Alexandria Engrg. J., 55(4), pp.3053~3059 (2016)[DOI]
  2. R. A. Cerutti, "On the k-Bessel functions", Int. Math. Forum, 7(37-40), pp.1851~1857 (2012)
  3. M. Chand, "Fractional integrals and solution of fractional kinetic equations involving k-Mittag-Leffer function", Trans. A. Razmadze Math. Inst., 171(2), pp.144~166 (2017)[DOI]
  4. R. Diaz, "On hypergeometric functions and Pochhammer k-symbol", Divulg. Mat., 15(2), pp.179~192 (2007)
  5. I. S. Gradshteyn, "Table of Integrals, Series, and Products" (2000), Academic Press
  6. A. A. Kilbas, "Generalized fractional integration of Bessel function of the first kind", Integral Transforms Spec. Funct., 19(11-12), pp.869~883 (2008)[DOI]
  7. V. Kiryakova, "All the special functions are fractional differintegrals of elementary functions", J. Phys. A, 30(14), pp.585~5103 (1997)[DOI]
  8. K. S. Miller, "An Introduction to Fractional Calculus and Fractional Dif- ferential Equations" (1993), A Wiley-Interscience Publication, John Wiley and Sons
  9. L. G. Romero, "Fractional Fourier transform and special k-functions", Int. J. Contemp. Math. Sci., 7(13-16), pp.693~704 (2012)
  10. L. G. Romero, "A new fractional Fourier transform and convolution products", Int. J. Pure Appl. Math., 66(4), pp.397~408 (2011)
  11. L. G. Romero, "The k-Bessel function of the first kind", Int. Math. Forum, 7(37-40), pp.1859~1864 (2012)
  12. I. N. Sneddon, "The Use of Integral Transforms" (1979), Tata McGraw-Hill
  13. M. R. Spiegel, "Theory and Problems of Laplace Transforms" (1965), Schaum Publishing Co.
  14. H. M. Srivastava, "Zeta and q-Zeta Functions and Associated Series and Integrals" (2012), Elsevier, Inc.
  15. H. M. Srivastava, "Multiple Gaussian Hypergeometric Series, Ellis Horwood Series: Mathematics and its Applications" (1985), Ellis Horwood Ltd.
  16. H. M. Srivastava, "Some fractional-calculus results for the H- function associated with a class of Feynman integrals", Russ. J. Math. Phys., 13(1), pp.94~100 (2006)[DOI]

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