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Volume 38, Issue 3
$(p, q)$-Analogue of Mittag-Leffler Function with $(p, q)$-Laplace Transform

Alok Jain, Altaf Ahmad Bhat, Renu Jain & Deepak Kumar Jain

DOI: 10.4208/ata.OA-2018-0014

Anal. Theory Appl., 38 (2022), pp. 351-360.

Published online: 2022-07

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  • Abstract

The aim of this paper is to define $(p, q)$-analogue of Mittag-Leffler Function, by using $(p, q)$-Gamma function. Some transformation formulae are also derived by using the $(p, q)$-derivative. The $(p, q)$-analogue for this function provides elegant generalization of $q$-analogue of Mittag-Leffler function in connection with $q$-calculus. Moreover, the $(p, q)$-Laplace Transform of the Mittag-Leffler function has been obtained. Some special cases have also been discussed.

  • Keywords

$(p, q)$-analogue of Mittag-Leffler function, $(p, q)$-Gamma function, $q$-calculus, $(p, q)$-derivative operator, $(p, q)$-Laplace transform.

  • AMS Subject Headings

33D05, 33D15, 33D60, 33C20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-38-351, author = {Jain , AlokBhat , Altaf AhmadJain , Renu and Jain , Deepak Kumar}, title = {$(p, q)$-Analogue of Mittag-Leffler Function with $(p, q)$-Laplace Transform}, journal = {Analysis in Theory and Applications}, year = {2022}, volume = {38}, number = {3}, pages = {351--360}, abstract = {

The aim of this paper is to define $(p, q)$-analogue of Mittag-Leffler Function, by using $(p, q)$-Gamma function. Some transformation formulae are also derived by using the $(p, q)$-derivative. The $(p, q)$-analogue for this function provides elegant generalization of $q$-analogue of Mittag-Leffler function in connection with $q$-calculus. Moreover, the $(p, q)$-Laplace Transform of the Mittag-Leffler function has been obtained. Some special cases have also been discussed.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-2018-0014}, url = {http://global-sci.org/intro/article_detail/ata/20806.html} }
TY - JOUR T1 - $(p, q)$-Analogue of Mittag-Leffler Function with $(p, q)$-Laplace Transform AU - Jain , Alok AU - Bhat , Altaf Ahmad AU - Jain , Renu AU - Jain , Deepak Kumar JO - Analysis in Theory and Applications VL - 3 SP - 351 EP - 360 PY - 2022 DA - 2022/07 SN - 38 DO - http://doi.org/10.4208/ata.OA-2018-0014 UR - https://global-sci.org/intro/article_detail/ata/20806.html KW - $(p, q)$-analogue of Mittag-Leffler function, $(p, q)$-Gamma function, $q$-calculus, $(p, q)$-derivative operator, $(p, q)$-Laplace transform. AB -

The aim of this paper is to define $(p, q)$-analogue of Mittag-Leffler Function, by using $(p, q)$-Gamma function. Some transformation formulae are also derived by using the $(p, q)$-derivative. The $(p, q)$-analogue for this function provides elegant generalization of $q$-analogue of Mittag-Leffler function in connection with $q$-calculus. Moreover, the $(p, q)$-Laplace Transform of the Mittag-Leffler function has been obtained. Some special cases have also been discussed.

Jain , AlokBhat , Altaf AhmadJain , Renu and Jain , Deepak Kumar. (2022). $(p, q)$-Analogue of Mittag-Leffler Function with $(p, q)$-Laplace Transform. Analysis in Theory and Applications. 38 (3). 351-360. doi:10.4208/ata.OA-2018-0014
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