Fractional Calculus of Extended Mittag-Leffler Function and Its Applications to Statistical Distribution

Abstract

Several fractional calculus operators have been introduced and investigated. In this sequence, we aim to establish the Marichev-Saigo-Maeda (MSM) fractional calculus operators and Caputo-type MSM fractional differential operators of extended Mittag-Leffler function (EMLF). We also investigate the statistical distribution associated with the EMLF. Finally, we derive some of the particular cases of the main results.

Keywords

• extended Mittag-Leffler function
• Wright-type hypergeometric functions
• extended Wright-type hypergeometric functions
• statistical distribution