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On certain dual
$q$-integral equations
Ola A. Ashour, Mourad E. H. Ismail and Zeinab S. Mansour |
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Vol. 275 (2015), No. 1, 63–102
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Abstract |
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We consider three different systems of dual -integral equations where the kernel is the third Jackson -Bessel functions. We solve the first system by applying the multiplying factor method (ansatz solution) and the second by employing the fractional -calculus, and we use the -Mellin transform to reduce the third system to a Fredholm -integral equation of the second kind. Examples are included. |
Keywords
$q$-Fourier transform, fractional $q$-integral operator,
$q$-special functions, $q$-dual integral equations
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Mathematical Subject Classification 2010
Primary: 45F10
Secondary: 34B30, 31B10, 26A33, 35R11
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Milestones
Received: 10 February 2014
Revised: 4 July 2014
Accepted: 7 July 2014
Published: 12 April 2015
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Authors |
| Ola A. Ashour | |
| Department of Mathematics, Faculty
of Science Cairo University P. O. Box 12613 Giza 12613 Egypt |
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| Mourad E. H. Ismail | |
| Department of Mathematics University of Central Florida 4000 Central Florida Boulevard P. O. Box 161364 Orlando, FL 32816-1364 United States |
Department of Mathematics Faculty of Science King Saud University P. O. Box 2455 Riyadh 11451 Saudi Arabia |
| Zeinab S. Mansour | |
| Department of Mathematics Faculty of Science King Saud University P. O. Box 2455 Riyadh 11451 Saudi Arabia |
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