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Image formulas and graphical interpretation of fractional derivatives of R-function and G-function

Praveen Agarwal|K.S. NISAR|Shilpi Jain|Mehar Chand|Guotao Wang
장전수학회 (Jangjeon Mathematical Society)|2016.10|Advanced Studies in Contemporary Mathematics|제26권 제4호|pp. 633-652

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키워드

Fractional integral operatorsSpecial functionsR-FunctionG-Function
주제분류수학

초록

In this paper, our main objective is to establish certain new image formulas of R- and G-functions by applying the operators of fractional derivative involving Appell's function F3(.) due to Saigo-Maeda and the main results interpreted graphically by implementing the MatLab(R2012a). Furthermore, by employing some integral transforms on the resulting formulas, we presented some more image formulas. All the results derived here are of general character and can yield a number of (known and new) results in the theory of special functions.

Abstract

In this paper, our main objective is to establish certain new image formulas of R- and G-functions by applying the operators of fractional derivative involving Appell's function F3(.) due to Saigo-Maeda and the main results interpreted graphically by implementing the MatLab(R2012a). Furthermore, by employing some integral transforms on the resulting formulas, we presented some more image formulas. All the results derived here are of general character and can yield a number of (known and new) results in the theory of special functions.

참고문헌 (22)

  1. Agarwal, P, "SD: The unified pathway fractional integral formulae", J. Fract. Calc. Appl, 4(9), pp.1~8 (2013)
  2. Choi, J, "Some new Saigo type fractional integral inequalities and their q-analogues", Abstr. Appl. Anal, 2014 (2014)
  3. 최준상, "Certain Fractional Integral Inequalities Involving Hypergeometric Operators", East Asian Mathematical Journal, 30(3), pp.283~291 (2014), 영남수학회[DOI]
  4. 최준상, "CERTAIN NEW PATHWAY TYPE FRACTIONAL INTEGRAL INEQUALITIES", 호남수학학술지, 36(2), pp.455~465 (2014), 호남수학회
  5. Choi, J, "Certain integral transform and fractional integral formulas for the generalized Gauss hypergeometric functions", Abstr. Appl. Anal, 2014 (2014)
  6. Kumar, D, "Generalized fractional differentiation of the H-function involving general class of polynomials", Int. J. Pure Appl. Sci. Technol, 16(1), pp.42~53 (2013)
  7. Srivastava, HM, "Certain fractional integral operators and the generalized incomplete hypergeometric functions", Appl. Appl. Math, 8(2), pp.333~345 (2013)
  8. Yang, AM, "Application of local fractional series expansion method to solve Klein-Gordon equations on Cantor sets", Abstr. Appl. Anal, 2014 (2014)
  9. M. Benchohra, "Existence and Uniqueness of solutions to impulsive fractional differential equations", Electronic Journal of Differential Equations, 10, pp.111~ (2009)
  10. A. Chouhan, "An alternative method for solving generalized differ-ential equations of fractional order", Kragujevac Journal of Mathematics, 37(2), pp.299~306 (2013)
  11. A. Chouhan, "On solution of generalized kinetic equation of fractional order", Int. Jr. of Mathematical Sciences and Applications, 2(2), pp.813~818 (2012)
  12. A. Chouhan, "On generalized Mittag-Leer function and fractional operators", IJCA Proceedings on National Conference on Advances in Technology and Applied Sciences NCATAS, (1), pp.9~12 (2014)
  13. R. Hilfer, "Application of Fractional Calculus in Physics" (2000), World Scientific Publishing Company
  14. A. A. Kilbas, "Generalized fractional integration of Bessel function of first kind", Integral transform and Spec. Funct, 19(12), pp.869~883 (2008)
  15. A. A. Kilbas, "Euler-type non-homogeneous differential equations with three Liouville fractional derivatives", Fract. Calc. Appl. Anal, 12(2), pp.205~233 (2009)
  16. Generalized functions for the fractional calculus, National Aero-nautics and Space Administration, "C. F. Lorenzo", Glenn Research Center, ~ (1999)
  17. R. K. Raina, "On the Weyl fractional operators of two-dimensions", C.R. Acad. Bulg. Sci, 36, pp.1273~1276 (1983)
  18. M. Saigo, "Application of generalized fractional calculus in the solution of an integral equation", J. Fractional Calculus, 14, pp.53~63 (1998)
  19. M. Saigo - N, "Maeda, More generalization of fractional calculus", Transform Metods and Special Functions, Varna, 1996 Proc. 2nd Intern. Workshop, pp.386~400 (1996), IMI-BAS
  20. R. K. Saxena - M, "Saigo, Generalized fractional calculus of the H-function associated with the Appell function", J. Frac. Calc, 19, pp.89~104 (2001)
  21. I. N. Sneddon, "The Use of Integral Transforms" (1979), Tata McGraw-Hill
  22. E.M. Wright, "The asymptotic expansion of the generalized hypergeometric function", Proc. London Math. Soc, 46, pp.389~408 (1946)

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