Scientific Research

An Academic Publisher

Solution of Some Integral Equations Involving Confluent *k*-Hypergeometric Functions

**Author(s)**Leave a comment

The principle aim of this research article is to investigate the properties of k-fractional integration introduced and defined by Mubeen and Habibullah [1],and secondly to solve the integral equation of the form

, for k > 0, β > 0, y > 0, 0 < x < t < ∞, where is the confluent k-hypergeometric functions, by using k-fractional integration.

, for k > 0, β > 0, y > 0, 0 < x < t < ∞, where is the confluent k-hypergeometric functions, by using k-fractional integration.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

S. Mubeen, "Solution of Some Integral Equations Involving Confluent

*k*-Hypergeometric Functions,"*Applied Mathematics*, Vol. 4 No. 7A, 2013, pp. 9-11. doi: 10.4236/am.2013.47A003.

[1] | S. Mubeen and G. M. Habibullah, “k-Fractional Integrals and Application,” International Journal of Contemporary Mathematical Sciences, Vol. 7, No. 2, 2012, pp. 89-94. |

[2] | A. Erdélyi, “An Integral Equation Involving Legendre Functions,” Journal of the Society for Industrial and Applied Mathematics, Vol. 12, No. 1, 1964, pp. 15-30. doi:10.1137/0112002 |

[3] | E. R. Love, “Some Integral Equations Involving Hypergeometric Functions,” Proceedings of the Edinburgh Mathematical Society, Vol. 15, No. 3, 1967, pp. 169-198. doi:10.1017/S0013091500011706 |

[4] | G. M. Habibullah, “Some Integral Equations Involving Confluent Hypergeometric Functions,” The Yokohama Mathematical Journal, Vol. 19, 1971, pp. 35-43. |

[5] | K. N. Srivastava, “Fractional Integration and Integral Equations with Polynomial Kernels,” Journal of the Society for Industrial and Applied Mathematics, Vol. 40, 1965, pp. 435-440. |

[6] | R. Diaz and C. Teruel, “q,k-Generalized Gamma and Beta Functions,” Journal of Nonlinear Mathematical Physics, Vol. 12, No. 1, 2005, pp. 118-134. doi:10.2991/jnmp.2005.12.1.10 |

[7] | R. Diaz and E. Pariguan, “On Hypergeometric Functions and Pochhammer k-Symbol,” Divulgaciones Matemáticas, Vol. 15, No. 2, 2007, pp. 179-192. |

[8] | R. Diaz, C. Ortiz and E. Pariguan, “On the k-Gamma q-Distribution,” Central European Journal of Mathematics, Vol. 8, No. 3, 2010, pp. 448-458. doi:10.2478/s11533-010-0029-0 |

[9] | M. Mansour, “Determining the k-Generalized Gamma Function Γk(x) by Functional Equations,” International Journal of Contemporary Mathematical Sciences, Vol. 4, No. 21, 2009, pp. 1037-1042. |

[10] | C. G. Kokologiannaki, “Properties and Inequalities of Generalized k-Gamma, Beta and Zeta Functions,” International Journal of Contemporary Mathematical Sciences, Vol. 5, No. 13-16, 2010, pp. 653-660. |

[11] | V. Krasniqi, “A Limit for the k-Gamma and k-Beta Function,” International Mathematical Forum, Vol. 5, No. 33, 2010, pp. 1613-1617. |

[12] | V. Krasniqi, “Inequalities and Monotonicity for the Ration of k-Gamma Function,” Scientia Magna, Vol. 6, No. 1, 2010, pp. 40-45. |

[13] | F. Merovci, “Power Product Inequalities for the Γk Function,” International Journal of Mathematical Analysis, Vol. 4, No. 21-24, 2010, pp. 1007-1012. |

[14] | S. Mubeen and G. M. Habibullah, “An Integral Representation of Some k-Hypergeometric Functions,” International Mathematical Forum, Vol. 7, No. 4, 2012, pp. 203-207. |

[15] | S. Mubeen, “k-Analogue of Kummer’s First Formula,” Journal of Inequalities and Special Functions, Vol. 3, No. 3, 2012, pp. 41-44. |

Copyright © 2018 by authors and Scientific Research Publishing Inc.

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.