Open AccessExtended Riemann Integral Equations Involving Generalized k−hypergeometric Function
Author(s) -
Aneela Nadir
Publication year - 2022
Publication title -
the punjab university journal of mathematics
Language(s) - English
Resource type - Journals
ISSN - 1016-2526
DOI - 10.52280/pujm.2022.540305
Subject(s) - mathematics , fredholm integral equation , integral equation , hypergeometric function , hypergeometric distribution , riemann hypothesis , kernel (algebra) , mathematical analysis , summation equation , riemann's differential equation , function (biology) , riemann integral , pure mathematics , mathematical physics , riemann xi function , singular integral , evolutionary biology , biology
This research proves the existence of the solution for the Fredholm integral equation of the first kind. Initially, k−Riemann integralequation is considered involving the k−hypergeometric function as kernel. k−fractional integration defined by Mubeen and Habibullah [16] isused to investigate the solution of the integral equationZ x0(x − t)ck −1Γk(c)q+1Fq,k Ã(ai, k),(b, k)(ci, k); 1 −xt!f(t)dt = g(x)where λ, ai, b, ci > 0, i = 1, . . . , q and f ∈ C◦.To prove the existence of solution, necessary and sufficient conditions aredefined.Keywords: k−Pochhammer symbol, k−hypergeometric function, k−FractionalIntegration, k−Riemann integral equation, Fredholm integral equation