Fractional calculus of the extended Bessel-Wright function and its applications to fractional kinetic equations
Chaudhary, M., Abubakar, U. (2023). Fractional calculus of the extended Bessel-Wright function and its applications to fractional kinetic equations. EKB Journal Management System, 14(2), 1-17. doi: 10.21608/jfca.2023.206432.1015
M.P. Chaudhary; U.M. Abubakar. "Fractional calculus of the extended Bessel-Wright function and its applications to fractional kinetic equations". EKB Journal Management System, 14, 2, 2023, 1-17. doi: 10.21608/jfca.2023.206432.1015
Chaudhary, M., Abubakar, U. (2023). 'Fractional calculus of the extended Bessel-Wright function and its applications to fractional kinetic equations', EKB Journal Management System, 14(2), pp. 1-17. doi: 10.21608/jfca.2023.206432.1015
Chaudhary, M., Abubakar, U. Fractional calculus of the extended Bessel-Wright function and its applications to fractional kinetic equations. EKB Journal Management System, 2023; 14(2): 1-17. doi: 10.21608/jfca.2023.206432.1015

Fractional calculus of the extended Bessel-Wright function and its applications to fractional kinetic equations

Journal of Fractional Calculus and Applications
Volume 14, Issue 2, July 2023, Page 1-17  XML PDF (471.88 K)
Document Type: Regular research papers
DOI: 10.21608/jfca.2023.206432.1015
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Authors
M.P. Chaudhary email 1; U.M. Abubakarorcid 2
1ISRWO, New Delhi, India
2Aliko Dangote University of Science and Technology, Wudil P.M.B.: 3244 Kano, Kano State-Nigeria.
Abstract
In this article, first of all we introduced a new concept for the $(p,q;\vartheta)$-extended Bessel-Wright function $J_{\omega;p,q}^{\sigma;\varsigma,\lambda}(z;\vartheta)$, and further discussed some new properties related to Marichev-Saigo-Maede fractional integral as well as their derivative operators, and also studied about the Caputo-type Marichev-Saigo-Maede fractional integral and its derivative operators which are applied to the $(p,q;\vartheta)$-extended Bessel-Wright function. Further, we have also discussed some special cases such as particular results on Saigo, Riemann-Liouville and Erdeyi-Kober fractional integrals and their derivative operators are obtained. As part of applications of the new $(p,q;\vartheta)$-extended Bessel-Wright function $J_{\omega;p,q}^{\sigma;\varsigma,\lambda} (z;\vartheta)$ to the fractional kinetic equations are also discussed in brief suggesting its possible solutions, please note that our current findings are based upon earlier findings of several researchers on various special functions such as Mittag-Leffler-type, $K$-type, $H$-type, $I$-type Bessel-type, Aleph-type, $S$-type, hypergeometric-type, and plenty of others (see Kiryakova \cite{AK3, AK6, AK8}), and integral transform such as Laplace, Sumudu were used by different researchers to study fractional kinetic equations.
Keywords
Beta function; Bessel-Struve function; Bessel-Wright function; Fox-Wright function
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