Integral transforms of an extended generalized multi-index Bessel function

AIMS Mathematics

Shahid Mubeen¹  Rana Safdar Ali¹  Iqra Nayab²  Gauhar Rahman³  Thabet Abdeljawad⁴  Kottakkaran Sooppy Nisar⁵ 

[1] 1 Department of Mathematics, University of Sargodha, Sargodha, Pakistan;2 Department of Mathematics, University of Lahore, Sargodha, Pakistan;3 Department of Mathematics, Shaheed Benazir Bhutto University, Sheringal, Upper Dir, 18000, Pakistan;4 Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, KSA 5 Department of Medical Research, China Medical University, Taichung 40402, Taiwan;6 Department of Mathematics, College of Arts and Sciences, Wadi Aldawser, 11991, Prince Sattam bin Abdulaziz University, Saudi Arabia;

关键词: extended multi-index bessel function;    fractional integrals and derivatives;    appell function;    extended beta transform;   

DOI  :  10.3934/math.2020482

来源: DOAJ

【 摘 要 】

In this paper, we discuss the extended generalized multi-index Bessel function by using the extended beta type function. Then we investigate its several properties including integral representation, derivatives, beta transform, Laplace transform, Mellin transforms, and some relations of extension of extended generalized multi-index Bessel function (E¹GMBF) with the Laguerre polynomial and Whittaker functions. Further, we also discuss the composition of the generalized fractional integral operator having Appell function as a kernel with the extension of extended generalized multi-index Bessel function and establish these results in terms of Wright functions.

【 授权许可】

Unknown