Work

On extended $ k $ -generalized Mittag-Leffler function and its properties

Year: 2023

Type: article

Abstract: In this current paper, we are using the concept of extension of the beta function to define an extended $ k $-generalized Mittag-Leffler function (GMLf) $ E_{k, l, m}^{\rho, \sigma;c}(x;p) $. There are four sections included in this paper containing some properties of the above-described function, like derivatives, integral representation, and integral transform. The establishment of some recurrence relations has also been done. We also derive the extended $ k $-GMLf from the extended $ k $-Riemann-Liouville (R-L) fractional derivative of generalized MLf. Numerous former results studied by many researchers can also be derived as special cases of our results.

Source: Mathematical Foundations of Computing

DOI: 10.3934/mfc.2023041

Authors: Shilpi Jain, B.B. Jaimini, Meenu Buri, Praveen Agarwal

Institutions: Poornima Institute of Engineering and Technology, Government College Kota, Peoples' Friendship University of Russia, Ajman University, Anand International College of Engineering

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: National Board for Higher Mathematics, RUDN University

Awards: G1969582618, G3600847317