TY - JOUR
T1 - Fractional differential equations for the generalized Mittag-Leffler function
AU - Agarwal, Praveen
AU - Al-Mdallal, Qasem
AU - Cho, Yeol Je
AU - Jain, Shilpi
N1 - Funding Information:
Authors would like to acknowledge and express their gratitude to the United Arab Emirates University, Al Ain, UAE for providing the financial support with Grant No. 31S240-UPAR (2) 2016.
Publisher Copyright:
© 2018, The Author(s).
PY - 2018/12/1
Y1 - 2018/12/1
N2 - In this paper, we establish some (presumably new) differential equation formulas for the extended Mittag-Leffler-type function by using the Saigo-Maeda fractional differential operators involving the Appell function F3(⋅) and results in terms of the Wright generalized hypergeometric-type function ψn+1({κl}l∈N0)m+1(z;p) recently established by Agarwal. Some interesting special cases are also pointed out.
AB - In this paper, we establish some (presumably new) differential equation formulas for the extended Mittag-Leffler-type function by using the Saigo-Maeda fractional differential operators involving the Appell function F3(⋅) and results in terms of the Wright generalized hypergeometric-type function ψn+1({κl}l∈N0)m+1(z;p) recently established by Agarwal. Some interesting special cases are also pointed out.
KW - fractional derivative operators
KW - generalized Gamma function
KW - generalized Mittag-Leffler function
KW - generalized Wright hypergeometric function
KW - generalized beta functions
UR - http://www.scopus.com/inward/record.url?scp=85042265626&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85042265626&partnerID=8YFLogxK
U2 - 10.1186/s13662-018-1500-7
DO - 10.1186/s13662-018-1500-7
M3 - Article
AN - SCOPUS:85042265626
SN - 1687-1839
VL - 2018
JO - Advances in Difference Equations
JF - Advances in Difference Equations
IS - 1
M1 - 58
ER -