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Certain Properties of Generalized q-Mittag–Leffler Type Function and its Application in Fractional q-Kinetic Equation

The present paper aims to introduce and study some properties and the applications of the q-analogue of the generalized Mittag–Leffler function γ , δ E α , β z . We establish several of its properties, including the convergence condition, the Caputo fractional q -derivative, the Hilfer fractional q...

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Bibliographic Details
Published in:International journal of applied and computational mathematics 2022-10, Vol.8 (5), Article 219
Main Authors: Bairwa, R. K., Kumar, Ajay, Kumar, Devendra
Format: Article
Language:English
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Summary:The present paper aims to introduce and study some properties and the applications of the q-analogue of the generalized Mittag–Leffler function γ , δ E α , β z . We establish several of its properties, including the convergence condition, the Caputo fractional q -derivative, the Hilfer fractional q -derivative, the Kober fractional q -integral, the Jackson q -integral, and the q -Sumudu transform. Furthermore, we study the applications of q-analogue of the generalized Mittag–Leffler function in kinetic equation and obtain the solution to the fractional q -kinetic equation includes this function and discuss certain special cases.
ISSN:2349-5103
2199-5796
DOI:10.1007/s40819-022-01387-1