Convolution integral equation of Fredholm type with certain trancedental functions

Abstract

The aim of this paper is to establish a solution of a certain class of convolution integral equation of Fredholm type whose kernel involve certain product of special function by using Riemann-Liouville and Weyl fractional integral operators. Some interesting particular cases are also considered.

Fredholm type integral equation with special functions

“…The integral equations occur in many fields of physics, mechanics and applied mathematics. In the last several years a large number of Fredholm type integral equations involving various polynomials or special functions as kernels have been studied by many authors notably Chaurasia et al [7,8], Buchman [4], Higgins [10], Love [16,17], Prabhakar and Kashyap [20] and others. In the present paper, we obtain the solutions of following Fredholm integral equation.…”

“…where φ 1 , φ i and a s are defined respectively by (7), (8) and (18). Also, provided that (a) (α) > (β),…”