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SOME INTEGRAL TRANSFORMS AND FRACTIONAL INTEGRAL FORMULAS FOR THE EXTENDED HYPERGEOMETRIC FUNCTIONS
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 Title & Authors
SOME INTEGRAL TRANSFORMS AND FRACTIONAL INTEGRAL FORMULAS FOR THE EXTENDED HYPERGEOMETRIC FUNCTIONS
Agarwal, Praveen; Choi, Junesang; Kachhia, Krunal B.; Prajapati, Jyotindra C.; Zhou, Hui;
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 Abstract
Integral transforms and fractional integral formulas involving well-known special functions are interesting in themselves and play important roles in their diverse applications. A large number of integral transforms and fractional integral formulas have been established by many authors. In this paper, we aim at establishing some (presumably) new integral transforms and fractional integral formulas for the generalized hypergeometric type function which has recently been introduced by Luo et al. [9]. Some interesting special cases of our main results are also considered.
 Keywords
gamma function;beta function;extended beta function;generalized hypergeometric functions;extended generalized hypergeometric functions;decomposition formula;integral transforms;fractional integral operators;
 Language
English
 Cited by
 References
1.
P. Agarwal, Further results on fractional calculus of Saigo operators, Appl. Appl. Math. 7 (2012), no. 2, 585-594.

2.
P. Agarwal, Certain properties of the generalized Gauss hypergeometric functions, Appl. Math. Inf. Sci. 8 (2014), no. 5, 2315-2320. crossref(new window)

3.
P. Agarwal and S. Jain, Further results on fractional calculus of Srivastava polynomials, Bull. Math. Anal. Appl. 3 (2011), no. 2, 167-174.

4.
M. A. Chaudhary, A. Qadir, M. Rafique, and S. M. Zubair, Extension of Euler's beta function, Appl. Math. Comput. 159 (2004), no. 2, 589-602.

5.
M. A. Chaudhary, A. Qadir, H. M. Srivastava, and R. B. Paris, Extended hypergeometric and confluent hypergeometric functions, J. Comput. Appl. Math. 78 (1997), no. 1, 19-32. crossref(new window)

6.
J. Choi and P. Agarwal, Certain Integral transform and fractional integral formulas for the generalized Gauss hypergeometric functions, Abstr. Appl. Anal. 2014 (2014), Article ID 735946, 7 pages.

7.
A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematical Studies, Elsevier Science, Amsterdem, The Netherlands, 2006.

8.
D. M. Lee, A. K. Rathie, R. K. Parmar, and Y. S. Kim, Genearlization of extended beta function, hypergeometric and confluent hypergeometric functions, Honam Math. J. 33 (2011), no. 2, 187-206. crossref(new window)

9.
M. J. Luo, G. V. Milovanovic, and P. Agarwal, Some results on the extended beta and extended hypergeometric functions, Appl. Math. Comput. 248 (2014), 631-651.

10.
A. M. Mathai and R. K. Saxena, Genearlized Hypergeometric Functions with Applications in Statistics and Physical Sciences, Springer-Verlag, Lecture Notes Series No. 348, Heidelberg, 1973.

11.
A. M. Mathai, R. K. Saxena, and H. J. Haubold, The H-Function Theory and Applications, Springer-Verlag New York, 2010.

12.
E. Ozergin, M. A. Ozarslan, and A. ALtin, Extension of gamma, beta and hypergeometric functions, J. Comput. Appl. Math. 235 (2011), no. 16, 4601-4610. crossref(new window)

13.
T. Pohlen, The Hadamard Product and Universal Power Series, Dissertation, Universit at Trier, 2009.

14.
I. N. Sneddon, The Use of Integral Transform, Tata McGraw-Hill, New Delhi, India, 1979.

15.
H. M. Srivastava and P. Agarwal, Certain fractional integral operators and the generalized incomplete hypergeometric functions, Appl. Appl. Math. 8 (2013), no. 2, 333-345.

16.
H. M. Srivastava, P. Agarwal, and S. Jain, Generating functions for the generalized Gauss hypergeometric functions, Appl. Math. Comput. 247 (2014), 348-352.

17.
H. M. Srivastava and J. Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Science, Amsterdam, The Netherlands, 2012.