The generalized fractional calculus operators introduced by Saigo and Maeda in 1996 will
be examined and further explored in this paper. By combining an incomplete ℵ-function with …

Many authors have introduced and investigated certain extended fractional derivative
operators. The main object of this paper is to give an extension of the Riemann-Liouville …

In this paper, our principle aim is to establish a new extension of the Caputo fractional
derivative operator involving the generalized hypergeometric type function F p (a, b; c; z; k) …

In this paper, an extension of Caputo fractional derivative operator is introduced, and the
extended fractional derivatives of some elementary functions are calculated. At the same …

The periodic and quasi-periodic solutions of the integrable system have been studied for
four decades based on the Riemann theta functions. However, there is a fundamental …

This paper introduces a new incomplete I− functions. The incomplete I− function is an
extension of the I− function given by Saxena [1] which is a extension of a familiar Fox's H …

This study investigates the solutions of an impulsive fractional differential equation
incorporated with a pantograph. This work extends and improves some results of the …

When the literature is examined, it is seen that there are many studies on the generalizations
of gamma, beta and hypergeometric functions. In this paper, new types of generalized …

In this paper, we reconstruct the gamma and beta functions using a general kernel function
in their integral representations. We also reconstruct the Gauss and confluent …

In this paper, we first introduce the incomplete extended Gamma and Beta functions with
matrix parameters; then, we establish some different properties for these new extensions …