Journal
COMPUTATIONAL & APPLIED MATHEMATICS
Volume 39, Issue 3, Pages -Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s40314-020-01224-5
Keywords
Mittag-Leffler functions; Fractional integrals; Fractional derivatives; Fractional differential equations; Bivariate Mittag-Leffler functions
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We define an analogue of the classical Mittag-Leffler function which is applied to two variables, and establish its basic properties. Using a corresponding single-variable function with fractional powers, we define an associated fractional integral operator which has many interesting properties. The motivation for these definitions is twofold: firstly, their link with some fundamental fractional differential equations involving two independent fractional orders, and secondly, the fact that they emerge naturally from certain applications in bioengineering.
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