Certain unified fractional integrals and derivatives for a product of Aleph function and a general class of multivariable polynomials

Journal of Inequalities and Applications

Volumn 2014, Issue 1, 2014, Pages

  Choi, Junesang ^a   Kumar, Dinesh ^b  

^a Dongguk University   (South Korea)

^b JAI NARAIN VYAS UNIVERSITY   (India)

Author keywords

a general class of multivariable polynomials; generalized Bessel Maitland function; generalized fractional calculus operators; generalized Wright hypergeometric function; H function; I function; Mittag Leffler function; function

Indexed keywords

EID: 84929377426     PISSN: 10255834     EISSN: 1029242X     Source Type: Journal    
DOI: 10.1186/1029-242X-2014-499     Document Type: Article

References (33)

1. Agarwal P, Purohit SD: The unified pathway fractional integral formulae.J. Fract. Calc. Appl. 2013,4(9):1–8.
2. Choi J, Agarwal P: Some new Saigo type fractional integral inequalities and theirq-analogues.Abstr. Appl. Anal. 2014., 2014: Article ID 579260
3. Choi J, Agarwal P: Certain fractional integral inequalities involving hypergeometric operators.East Asian Math. J. 2014, 30:283–291.
4. Choi J, Agarwal P: Certain new pathway type fractional integral inequalities.Honam Math. J. 2014, 36:437–447.
5. Choi J, Agarwal P: Certain integral transform and fractional integral formulas for the generalized Gauss hypergeometric functions.Abstr. Appl. Anal. 2014., 2014: Article ID 735946
6. Kumar D, Daiya J:Generalized fractional differentiation of the[InlineEquation not available: see fulltext.]-function involving general class of polynomials.Int. J. Pure Appl. Sci. Technol. 2013,16(1):42–53.
7. Srivastava HM, Agarwal P: Certain fractional integral operators and the generalized incomplete hypergeometric functions.Appl. Appl. Math. 2013,8(2):333–345.
8. Yang AM, Zhang YZ, Cattani C, Xie GN, Rashidi MM, Zhou YJ, Yang XJ: Application of local fractional series expansion method to solve Klein-Gordon equations on Cantor sets.Abstr. Appl. Anal. 2014., 2014: Article ID 37274
9. Love ER: Some integral equations involving hypergeometric functions.Proc. Edinb. Math. Soc. 1967,15(3):169–198.
10. Srivastava HM, Saxena RK: Operators of fractional integration and their applications.Appl. Math. Comput. 2001, 118:1–52.
11. Debnath L, Bhatta D: Integral Transforms and Their Applications. Chapman & Hall/CRC, Boca Raton; 2006.
12. Saxena RK, Daiya J, Kumar D:Fractional integration of the[InlineEquation not available: see fulltext.]-function and a general class of polynomials via pathway operator.J. Indian Acad. Math. 2013,35(2):261–274.
13. Saxena RK, Ram J, Chandak S, Kalla SL: Unified fractional integral formulae for the Fox-Wright generalized hypergeometric function.Kuwait J. Sci. Eng. 2008,35(1A):1–20.
14. Saxena RK, Ram J, Kumar D: Generalized fractional differentiation for Saigo operators involving Aleph-function.J. Indian Acad. Math. 2012,34(1):109–115.
15. Saxena RK, Ram J, Kumar D:Generalized fractional differentiation of the Aleph-function associated with the Appell function[InlineEquation not available: see fulltext.].Acta Cienc. Indica 2012,38(4):781–792.
16. Saigo M: A remark on integral operators involving the Gauss hypergeometric functions.Math. Rep. Coll. Gen. Educ. Kyushu Univ. 1978, 11:135–143.
17. Samko SG, Kilbas AA, Marichev OI: Fractional Integrals and Derivatives: Theory and Applications. Gordon & Breach, Yverdon; 1993.
18. Miller KS, Ross B: An Introduction to Fractional Calculus and Fractional Differential Equations. Wiley, New York; 1993.
19. Ram J, Kumar D: Generalized fractional integration of the ℵ-function.J. Rajasthan Acad. Phys. Sci. 2011,10(4):373–382.
20. Saigo M, Maeda N: More generalization of fractional calculus.Transform Methods and Special Functions 1996, 386–400. Varna, Bulgaria
21. Srivastava HM, Karlsson PW: Multiple Gaussian Hypergeometric Series. Ellis Horwood, Chichester; 1985.
22. Srivastava HM, Choi J: Zeta and q-Zeta Functions and Associated Series and Integrals. Elsevier, Amsterdam; 2012.
23. Saxena RK, Saigo M: Generalized fractional calculus of theH-function associated with the Appell function.J. Fract. Calc. 2001, 19:89–104.
24. Saxena RK, Pogány TK: On fractional integration formulae for Aleph functions.Appl. Math. Comput. 2011, 218:985–990.
25. Saxena RK, Pogány TK: Mathieu-type series for the ℵ-function occurring in Fokker-Planck equation.Eur. J. Pure Appl. Math. 2010,3(6):980–988.
26. Saxena RK, Ram J, Kumar D: On the two-dimensional Saigo-Maeda fractional calculus associated with two-dimensional Aleph transform.Matematiche 2013, 68:267–281.
27. Saxena RK, Ram J, Kumar D:Generalized fractional integration of the product of two ℵ-functions associated with the Appell function[InlineEquation not available: see fulltext.].ROMAI J. 2013,9(1):147–158.
28. Saxena RK, Ram J, Kumar D: Generalized fractional integral of the product of two Aleph-functions.Appl. Appl. Math. 2013,8(2):631–646.
29. Saxena VP: Formal solution of certain new pair of dual integral equations involvingH-functions.Proc. Nat. Acad. Sci. India Sect. A 1982, 51:366–375.
30. Mathai AM, Saxena RK, Haubold HJ: The H-Function: Theory and Applications. Springer, New York; 2010.
31. Srivastava HM, Garg M: Some integrals involving a general class of polynomials and the multivariableH-function.Rev. Roum. Phys. 1987, 32:685–692.
32. Srivastava HM: A contour integral involving Fox’sH-function.Indian J. Math. 1972, 14:1–6.
33. Srivastava HM, Saxena RK, Ram J: Some multidimensional fractional integral operations involving a general class of polynomials.J. Math. Anal. Appl. 1995, 193:373–389.