Punjab University Journal of Mathematics, Vol 54, No 3 (2022)

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Extended Riemann Integral Equations Involving Generalized k¡hypergeometric Functions

Aneela Nadir


This research proves the existence of the solution for the Fredholmintegral 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¡1¡k(c) q+1Fq;kÃ(ai; k); (b; k)(ci; k); 1 ¡xt!f(t)dt = g(x)where ¸; ai; b; ci > 0; i = 1; : : : ; q and f 2 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.

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