Concept Paper
Version 1
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The J-Generalized P - K Mittag-Leffler Function
Version 1
: Received: 2 May 2020 / Approved: 5 May 2020 / Online: 5 May 2020 (02:43:50 CEST)
How to cite: Gehlot, K.S.; Bhandari, A. The J-Generalized P - K Mittag-Leffler Function. Preprints 2020, 2020050054. https://doi.org/10.20944/preprints202005.0054.v1 Gehlot, K.S.; Bhandari, A. The J-Generalized P - K Mittag-Leffler Function. Preprints 2020, 2020050054. https://doi.org/10.20944/preprints202005.0054.v1
Abstract
We know that the classical Mittag-Leffler function play an important role as solution of fractional order differential and integral equations. We introduce the j-generalized p - k Mittag-Leffler function. We evaluate the second order differential recurrence relation and four different integral representations and introduce a homogeneous linear differential equation whose one of the solution is the j-generalized p-k Mittag-Leffler function. Also we evaluate the certain relations that exist between j-generalized p - k Mittag-Leffler function and Riemann-Liouville fractional integrals and derivatives. We evaluate Mellin-Barnes integral representation of j-generalized p-k Mittag-Le er Function. The relationship of j-generalized p-k Mittag-Leffler Function with Fox H-Function and Wright hypergeometric function is also establish. we obtained its Euler transform, Laplace Transform and Mellin transform. Finally we derive some particular cases.
Keywords
the j-generalized p - k Mittag-Lefflerr Function; the p - k Mittag-Leffler Function; generalized k-Mittag-Leffler Function; two parameter pochhammer symbol; two parameter Gamma function
Subject
Computer Science and Mathematics, Analysis
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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