Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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A NEW EXTENSION OF THE MITTAG-LEFFLER FUNCTION

  • Arshad, Muhammad (Department of Mathematics International Islamic University) ;
  • Choi, Junesang (Department of Mathematics Dongguk University) ;
  • Mubeen, Shahid (Department of Mathematics University of Sargodha) ;
  • Nisar, Kottakkaran Sooppy (Department of Mathematics College of Arts and Science at Wadi Al-dawaser Prince Sattam bin Abdulaziz University) ;
  • Rahman, Gauhar (Department of Mathematics International Islamic University)
  • Received : 2017.05.22
  • Accepted : 2018.01.10
  • Published : 2018.04.30
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Abstract

Since Mittag-Leffler introduced the so-called Mittag-Leffler function in 1903, due to its usefulness and diverse applications, a variety and large number of its extensions (and generalizations) and variants have been presented and investigated. In this sequel, we aim to introduce a new extension of the Mittag-Leffler function by using a known extended beta function. Then we investigate ceratin useful properties and formulas associated with the extended Mittag-Leffler function such as integral representation, Mellin transform, recurrence relation, and derivative formulas. We also introduce an extended Riemann-Liouville fractional derivative to present a fractional derivative formula for a known extended Mittag-Leffler function, the result of which is expressed in terms of the new extended Mittag-Leffler functions.

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References

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