Abstract
This paper is devoted to the useful method of solving the one-dimensional integral equation of Fredholm type. The Mellin transform technique for solving a general fredholm type integral equation with the function and a generalized polynomial in the kernel is considered. By specializing the coefficients and various parameters in the generalized polynomials and function, our main theorem would readily yield several results involving simpler kernels.
Highlights
In the last several years a large number of Fredholm type integral equationsinvolving various polynomials or special functions as their kernels have beenstudied by many authors notablyRinku Jain and Kirti ArekarBuchman [10], Higgins [11], Love ([3] and[2), Prabhakar and Kashyap [12], Srivastava andRaina [6] and others
In the present paper, we obtain the following one dimensional Fredholm integral equation (1.1 ) involving the Յ -function and a generalised polynomials in the kernel can be solved by resorting to the application of Mellin transforms
The Aleph Յ-function occurring in (1.1) introduced by Sudland et al [ 9] which is defined as a contour integral of Mellin Barnes Type: א[Z
Summary
Buchman [10], Higgins [11], Love ([3] and[2), Prabhakar and Kashyap [12], Srivastava and. The Aleph Յ-function occurring in (1.1) introduced by Sudland et al [ 9] which is defined as a contour integral of Mellin Barnes Type: א[Z. The parameters pi, qi are non-negative integers satisfying 0 ≤ n ≤ pi, 1≤. The existence conditions for the defining integral (1.1) are given below:. The general polynomials of R variables given by Srivastava [4] defined and represented as : S m1,..., m n1,..., nR. Let denote the space of all functions f which are defined on R+ = [0 , ∞) and satisfy (i) f ∈ b∞ (R+),. For correspondence to the space of good functions defined on the whole real line (-∞ , ∞) see (Lighthill) [8]. 0 x for the Riemann-Liouville fractional integral operator defined by eq (1.8) above)
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