Fractional k-Calculus Approach to the Extended k-Hypergeometric Function

The primary objective of the present manuscript is to evaluate the left-sided and right-sided kSaigo k fractional differentiation and integration of the extended k-hypergeometric function. The study employs Saigo k-generalized fractional operators, incorporating the k-hypergeometric function within the kernel, to the extended k-hypergeometric function. Additionally, the paper explores special cases associated with k-Riemann-Liouville fractional calculus operators.