Two unified families of bivariate Mittag-Leffler functions

Cemaliye Kürt, Arran Fernandez and Mehmet Ali Özarslan

Applied Mathematics and Computation, 2023, vol. 443, issue C

Abstract: The various bivariate Mittag-Leffler functions existing in the literature are gathered here into two broad families. Several different functions have been proposed in recent years as bivariate versions of the classical Mittag-Leffler function; we seek to unify this field of research by putting a clear structure on it. We use our general bivariate Mittag-Leffler functions to define fractional integral operators (which have a semigroup property) and corresponding fractional derivative operators (which act as left inverses and analytic continuations). We also demonstrate how these functions and operators arise naturally from some fractional partial integro-differential equations of Riemann–Liouville type.

Keywords: Mittag-Leffler functions; Bivariate Mittag-Leffler functions; Fractional integrals; Fractional derivatives; Abel equations; Fractional differential equations (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:443:y:2023:i:c:s0096300322008530

DOI: 10.1016/j.amc.2022.127785

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