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

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.

33D05, 33D15, 33D60, 33C20

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@Article{ATA-38-351, author = {Alok and Jain and and 24114 and and Alok Jain and Altaf Ahmad and Bhat and and 24115 and and Altaf Ahmad Bhat and Renu and Jain and and 24116 and and Renu Jain and Deepak Kumar and Jain and and 24117 and and Deepak Kumar Jain}, 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.

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