Thai Journal of Mathematics Volume 15 (2017) Number 2 : 491–501 http://thaijmath.in.cmu.ac.th ISSN 1686-0209 Extension of Integral Equations of Fredholm Type Involving Special Functions V.B.L. Chaurasia † and Vinod Gill ‡, 1 † Department of Mathematics, University of Rajasthan, Jaipur-302004, Rajasthan, India. e-mail : drvblc@yahoo.com ‡ Department of Mathematics, Amity University Rajasthan Jaipur-302030, India. e-mail : vinod.gill08@gmail.com Abstract : Integral equations occur in many fields of mechanics and mathe- matical physics. But specially Fredholm integral equations arise in the theory of signal processing, most notably as the spectral concentration problem. They also commonly arise in linear forward modeling and inverse problems. In this paper we establish a solution of integral equation of Fredholm type whose kernel involve cer- tain product of special functions by using Riemann-Liouville and Weyl fractional integral operators. Keywords : Fredholm type integral equations; Riemann-Liouville fractional inte- gral; Weyl fractional integral; Mellin transform; multivariable I -function; general class of polynomials; generalized polynomials; I -function. 2010 Mathematics Subject Classification : 26A33; 33C99; 33E60; 33E70; 33E20; 45B05. 1 Introduction Fredholm type integral equations involving various polynomials or special func- tions as their kernel, have been studied by many authors notably Buchman [1], Fox [2], Higgins [3], Love [4, 5], Prabhakar and Kashyap [6], Srivastava and Buchman 1 Corresponding author. Copyright c  2017 by the Mathematical Association of Thailand. All rights reserved.