Some Results on Generalized Fractional Calculus Operators Associated with the Product of the General Class of Polynomials and Extended Mittag-Leffler Type Function
Bhupender Singh Shaktawat
*
Department of Mathematics, Dayanand College, Ajmer-305001, India.
*Author to whom correspondence should be addressed.
Abstract
The main objective of this paper is to evaluate four new image formulas utilizing generalized fractional calculus operators, which include both fractional integration and fractional differentiation operators. Specifically, these operators are applied to the product of a general class of polynomials (also known as Srivastava polynomials) and an extended Mittag-Leffler type function. The analytical results derived in this work are explicitly expressed in terms of the generalized Wright hypergeometric function. Due to the general nature and flexibility of the extended Mittag-Leffler type function, Srivastava polynomials, and Wright hypergeometric function, numerous existing formulas in the literature—as well as several new formulas—can be easily derived as special cases of our main findings. Overall, this work provides simple and useful theoretical tools that can be applied to fractional differential equations and mathematical physics.
Keywords: Generalized fractional calculus operators, extended Mittag-Leffler type function, generalized wright hypergeometric function, Srivastava polynomials and special functions