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## S-generalized Mittag-Leffler Function and its Certain Properties

#### Praveen AGARWAL [1] , Aysegul CETİNKAYA [2] , Shilpi JAİN [3] , İ. Onur KIYMAZ [4]

In 2014, S-generalized beta function which consist of
seven parameters, defined and studied by Srivastava et al. [H. M.
Srivastava, P. Agarwal and S. Jain, Generating functions for the
generalized Gauss hypergeometric functions, Appl. Math. Comput., 247 (2014), pp. 348-352]. In this paper, by using S-generalized
beta function, we introduce a new generalization of Mittag-Leffler
function. This new generalization of Mittag-Leffler function is consist of eleven parameters. We also investigate some of its certain
properties such as integral representations, recurrence formulas and
derivative formulas by using classical and fractional derivatives.
Furthermore, we determine its Mellin, beta and Laplace integral
transforms.

Mittag-Leffler function, generalized beta function, fractional derivative
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Primary Language en Engineering Articles Orcid: 0000-0001-7556-8942Author: Praveen AGARWAL Institution: Anand-ICECountry: India Orcid: 0000-0001-7498-328XAuthor: Aysegul CETİNKAYA (Primary Author)Institution: Ahi Evran UniversityCountry: Turkey Orcid: 0000-0003-1770-5309Author: Shilpi JAİN Institution: Poornima College of EngineeringCountry: India Orcid: 0000-0003-2375-0202Author: İ. Onur KIYMAZ Institution: Ahi Evern UniversityCountry: Turkey Department of Science \& Technology(DST), India and Science \& Engineering Research Board (SERB), India INT/RUS/RFBR/P-308 and TAR/2018/000001 The research was supported by the Department of Science \& Technology(DST), India (No:INT/RUS/RFBR/P-308) and Science \& Engineering Research Board (SERB), India (No:TAR/2018/000001). Publication Date : October 15, 2019
 Bibtex @research article { mathenot578638, journal = {Mathematical Sciences and Applications E-Notes}, issn = {}, eissn = {2147-6268}, address = {}, publisher = {Murat TOSUN}, year = {2019}, volume = {7}, pages = {139 - 148}, doi = {10.36753/mathenot.578638}, title = {S-generalized Mittag-Leffler Function and its Certain Properties}, key = {cite}, author = {AGARWAL, Praveen and CETİNKAYA, Aysegul and JAİN, Shilpi and KIYMAZ, İ. Onur} } APA AGARWAL, P , CETİNKAYA, A , JAİN, S , KIYMAZ, İ . (2019). S-generalized Mittag-Leffler Function and its Certain Properties. Mathematical Sciences and Applications E-Notes , 7 (2) , 139-148 . DOI: 10.36753/mathenot.578638 MLA AGARWAL, P , CETİNKAYA, A , JAİN, S , KIYMAZ, İ . "S-generalized Mittag-Leffler Function and its Certain Properties". Mathematical Sciences and Applications E-Notes 7 (2019 ): 139-148 Chicago AGARWAL, P , CETİNKAYA, A , JAİN, S , KIYMAZ, İ . "S-generalized Mittag-Leffler Function and its Certain Properties". Mathematical Sciences and Applications E-Notes 7 (2019 ): 139-148 RIS TY - JOUR T1 - S-generalized Mittag-Leffler Function and its Certain Properties AU - Praveen AGARWAL , Aysegul CETİNKAYA , Shilpi JAİN , İ. Onur KIYMAZ Y1 - 2019 PY - 2019 N1 - doi: 10.36753/mathenot.578638 DO - 10.36753/mathenot.578638 T2 - Mathematical Sciences and Applications E-Notes JF - Journal JO - JOR SP - 139 EP - 148 VL - 7 IS - 2 SN - -2147-6268 M3 - doi: 10.36753/mathenot.578638 UR - https://doi.org/10.36753/mathenot.578638 Y2 - 2019 ER - EndNote %0 Mathematical Sciences and Applications E-Notes S-generalized Mittag-Leffler Function and its Certain Properties %A Praveen AGARWAL , Aysegul CETİNKAYA , Shilpi JAİN , İ. Onur KIYMAZ %T S-generalized Mittag-Leffler Function and its Certain Properties %D 2019 %J Mathematical Sciences and Applications E-Notes %P -2147-6268 %V 7 %N 2 %R doi: 10.36753/mathenot.578638 %U 10.36753/mathenot.578638 ISNAD AGARWAL, Praveen , CETİNKAYA, Aysegul , JAİN, Shilpi , KIYMAZ, İ. Onur . "S-generalized Mittag-Leffler Function and its Certain Properties". Mathematical Sciences and Applications E-Notes 7 / 2 (October 2019): 139-148 . https://doi.org/10.36753/mathenot.578638 AMA AGARWAL P , CETİNKAYA A , JAİN S , KIYMAZ İ . S-generalized Mittag-Leffler Function and its Certain Properties. Math. Sci. Appl. E-Notes. 2019; 7(2): 139-148. Vancouver AGARWAL P , CETİNKAYA A , JAİN S , KIYMAZ İ . S-generalized Mittag-Leffler Function and its Certain Properties. Mathematical Sciences and Applications E-Notes. 2019; 7(2): 148-139.

Authors of the Article
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