Some Integral Transforms and Fractional Integral Formulas for the Extended Hypergeometric Functions (original) (raw)

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.

Key takeaways

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  1. Establish new integral transforms and fractional integral formulas for generalized hypergeometric functions.
  2. Generalized hypergeometric functions are crucial in mathematical physics and engineering applications.
  3. Three types of integral transforms connect Euler, Varma, Laplace, and Whittaker functions.
  4. The study includes fractional integral formulas using Saigo hypergeometric operators.
  5. Results extend to various families of generalized Gauss hypergeometric functions.

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References (17)

  1. P. Agarwal, Further results on fractional calculus of Saigo operators, Appl. Appl. Math. 7 (2012), no. 2, 585-594.
  2. Certain properties of the generalized Gauss hypergeometric functions, Appl. Math. Inf. Sci. 8 (2014), no. 5, 2315-2320.
  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.
  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 Frac- tional 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.
  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 Applica- tions 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 Applica- tions, Springer-Verlag New York, 2010.
  12. E. Özergin, M. A. Özarslan, and A. ALtin, Extension of gamma, beta and hypergeometric functions, J. Comput. Appl. Math. 235 (2011), no. 16, 4601-4610.
  13. T. Pohlen, The Hadamard Product and Universal Power Series, Dissertation, Univer- sität 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 general- ized 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. Praveen Agarwal Department of Mathematics Anand International College of Engineering Jaipur 303012, India E-mail address: goyal.praveen2011@gmail.com