본문 바로가기
KERD
논문KCI 등재

GENERALIZED FRACTIONAL CALCULUS FORMULAS INVOLVING THE PRODUCT OF ALEPH-FUNCTION AND SRIVASTAVA POLYNOMIALS

Dinesh Kumar|R.K.Gupta|B.S.Shaktawat|최준상
장전수학회 (Jangjeon Mathematical Society)|2017.10|Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집) (Proceedings of the Jangjeon Mathematical Society)|제20권 제4호|pp. 701-717|DOI 10.17777/pjms.2017.20.4.016

1

조회

0

다운로드

1

인용

0

참고문헌

키워드

Mittag-Leffler functionSaigo-Maeda fractional calculus operatorsAleph-function of one and two variablesI-functionH-functiongeneralized Wright hypergeometric function pΨq
주제분류수학

초록

The object of this paper is to establish four formulas for the Saigo-Maeda fractional calculus operators associated with product of the Aleph-function and the general class of polynomials (Srivastava polynomials), which are expressed in terms of the Aleph-function of two variables. Since the involved fractional calculus operators, the Alephfunction, and the Srivastava polynomials are very general, the main results here can be specialized to yield a large number of formulas for fractional calculus operators involving various special functions and polynomials. Here some special cases are demonstrated.

Abstract

The object of this paper is to establish four formulas for the Saigo-Maeda fractional calculus operators associated with product of the Aleph-function and the general class of polynomials (Srivastava polynomials), which are expressed in terms of the Aleph-function of two variables. Since the involved fractional calculus operators, the Alephfunction, and the Srivastava polynomials are very general, the main results here can be specialized to yield a large number of formulas for fractional calculus operators involving various special functions and polynomials. Here some special cases are demonstrated.

참고문헌 (30)

  1. D. Baleanu, "Generalized fractional integrals of product of two H-functions and a general class of polynomials", International Journal of Computer Mathematics, 93(8), pp.1320~1329 (2015), Informa UK Limited[DOI]
  2. J. Choi, "Certain unified fractional integrals and derivatives for a product of Aleph function and a general class of multivariable polynomials", J. Inequal. Appl, (2014), pp.15~ (2014)
  3. D. Kumar, "Generalized fractional integration of the H-function involving general class of polynomials", Walailak J. Sci. Tech, 11(12), pp.1019~1030 (2014)
  4. D. Kumar, "Certain generalized fractional differentiation of the product of two ℵ-functions associated with the Appell function F3", Appl. Math. Sci, 10(4), pp.187~196 (2016)
  5. D. Kumar, "Generalized fractional differentiation of the H-function involving general class of polynomials", Int. J. Pure Appl. Sci. Technol, 16(1), pp.42~53 (2013)
  6. D. Kumar, "Generalized fractional integrals involving product of multivariable H-function and a general class of polynomials", J. Nonlinear Sci. Appl, 9, pp.8~21 (2016)
  7. O. I. Marichev, "Volterra equation of Mellin convolution type with a Horn function in the kernel, Izvestiya Akademii Nauk BSSR", Seriya Fiziko-Matematicheskikh Nauk, 1, pp.128~129 (1994)
  8. 1978, , ~
  9. A. M. Mathai, "The H-function: Theory and Appli- cations" (2010), Springer
  10. K. S. Miller, "An Introduction to Fractional Calculus and Fractional Differential Equations" (1993), A Wiley-Interscience Publication, John Wiley and Sons
  11. J. Ram, "Generalized fractional integration of the ℵ-function", J. Ra- jasthan Acad. Phy. Sci, 10(4), pp.373~382 (2011)
  12. M. Saigo, "A remark on integral operators involving the Gauss hypergeometric functions", Math. Rep. College General Ed. Kyushu Univ, 11, pp.135~143 (1978)
  13. M. Saigo, "Generalized fractional calculus of the H-function", Fukuoka Univ. Sci. Reports, 29, pp.31~45 (1999)
  14. M. Saigo, "Transform Methods and Special Functions", pp.386~400 (1996)
  15. S. G. Samko, "Fractional Integrals and Derivatives: Theory and Applications" (1993), Gordon and Breach Science Publishers
  16. V. P. Saxena, "Formal solution of certain new pair of dual integral equations involving H-functions", Proc. Nat. Acad. Sci. India Sect. A, 51, pp.366~375 (1982)
  17. R. K. Saxena, "Fractional integration of the H-function and a general class of polynomials via pathway operator", J. Indian Acad. Math, 35(2), pp.261~274 (2013)
  18. R. K. Saxena, "Generalized fractional calculus of the Aleph-function involving a general class of polynomials", Acta Mathematica Scientia, 35B(5), pp.1095~1110 (2015)
  19. R. K. Saxena, "On fractional integration formulae for Aleph functions", Appl. Math. Comput, 218, pp.985~990 (2011)
  20. R. K. Saxena, "Generalized fractional differentiation for Saigo operators involving Aleph-function", J. Indian Acad. Math, 34(1), pp.109~115 (2012)
  21. R. K. Saxena, "Generalized fractional differentiation of the Aleph-function associated with the Appell function F3", Acta Ciencia Indica, 38 M(4), pp.781~792 (2012)
  22. R. K. Saxena, "On the two-dimensional Saigo-Maeda fractional calculus associated with two-dimensional Aleph transform", Le Matematiche, 68, pp.267~281 (2013)
  23. R. K. Saxena, "Generalized fractional integral of the product of two Aleph-functions", Appl. Appl. Math, 8(2), pp.631~646 (2013)
  24. H. M. Srivastava, "A contour integral involving Fox's H-function", Indian J. Math, 14, pp.1~6 (1972)
  25. H. M. Srivastava, "Some integrals involving a general class of polynomials and the multivariable H-function", Revista, Roumaine Physics, 32, pp.685~692 (1987)
  26. H. M. Srivastava, "The H-Functions of One and Two Variables with Applications" (1982), South Asian Publishers
  27. H. M. Srivastava, "Some multidimensional fractional integral operations involving a general class of polynomials", J. Math. Anal, Appl, 193, pp.373~389 (1995)
  28. H. M. Srivastava, "The integration of certain product of the multivariable H-function with a general class of polynomials", Rend. Circ. Mat. Palermo, 32, pp.157~187 (1983)
  29. N. Sudland, "Open problem: who knows about the Aleph (ℵ)-functions?", Fract. Calc. Appl. Anal, 1(4), pp.401~402 (1998)
  30. N. Sudland, "Fractional driftless Fokker-Planck equation with power law diffusion coefficients", Computer Algebra in Scientific Computing (CASC Konstanz 2001), pp.513~525 (2001), Springer

관련 논문AI추천

FRACTIONAL CALCULUS OPERATORS APPLIED TO THE FUNCTION INVOLVING THE PRODUCT OF SRIVASTAVA POLYNOMIALS AND INCOMPLETE I-FUNCTIONSK. JANGID, N.K. JANGID, S. ARACI, S.D. PUROHIT, S. JOSHI장전수학회 · Advanced Studies in Contemporary Mathematics2021 · 제31권 제2호Fractional calculus formulas involving $\overline{H}$-function and Srivastava polynomialsDinesh Kumar대한수학회 · 대한수학회논문집2016 · 제31권 제4호Some Finite Integrals Involving Srivastava's Polynomials and the Aleph FunctionAlok Bhargava, Amber Srivastava, Rohit Mukherjee경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2016 · 제56권 제2호Integral Formulas Involving Product of Srivastava's Polynomials and Galue type Struve FunctionsDaya Lal Suthar, Mitku Andualem경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2019 · 제59권 제4호Certain integral formulas associated with Aleph (ℵ)-functionErkinjon T. Karimov, Jyotindra C. Prajapati, Praveen Agarwal, Shilpi Jain대한수학회 · 대한수학회논문집2017 · 제32권 제2호A Study of Generalized Weyl Differintegral Operator Associated with a General Class of Polynomials and the Multivariable H-functionMonica Wiseman, Ramesh Chandra Soni경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2010 · 제50권 제2호

이 간행물의 다른 논문 (15건)

A NOTE ON DEGENERATE FUBINI POLYNOMIALS김대산, 장광우, 김택연pp. 521-531DEGENERATE COMPLETE BELL POLYNOMIALS AND NUMBERS김택연pp. 533-543Numerical solution of variational problems using exponential sextic splinePooja Khandelwal, Arshad Khanpp. 545-562CERTAIN CONDITIONS FOR MEAN CONVERGENCE OF HERMITE AND HERMITE-FEJER INTERPOLATION POLYNOMIALS WITH ERDOS-TYPE WEIGHTS정희선, RYOZI SAKAIpp. 563-582ON CHARACTER PSEUDO - AMENABLE SEMIGROUP ALGEBRASP. O. Olanipekun, O. T. Mewomo, A. A. Mebawondu, U. O. Adielepp. 583-593
원문 보기