2017/03/03 by Christian Lavault, Lavault, Christian
Mathematics · #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #FOS: Physical sciences #Fractional Differential Equations Solutions #Functional Analysis (math.FA) #Iterative Methods for Nonlinear Equations #Mathematical Physics (math-ph) #Mathematical functions and polynomials
paper · pdf · doi:10.48550/arxiv.1703.01912
openalex publication_date 2017/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, the generalized fractional integral operators of two generalized Mittag-Leffler type functions are investigated. The special cases of interest involve the generalized Fox--Wright function and the generalized M-series and K-function. In the next Section 2 we first recall some generalized fractional integral operators among the most widely used in fractional calculus. Section 3 is devoted to the definitions of M-series and K-function and their relations to special functions. In Sections 4 and 5, effective fractional calculus of the generalized M-series and the K-function is carried out. The last section briefly concludes and opens up new perspectives. The results established herein generalize recent properties of generalized Mittag-Leffler type functions using left-and right-sided generalized fractional differintegral operators. The note results also in important applications in physics and mathematical engineering.