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Bessel and Mittag-Leffler functions are prominent within
mathematical and scientific fields due to increasing interest in
non-conventional models within applied mathematics. Since the
analytical solutions of many differential and integral equations of
arbitrary order can be written as series of special functions of
fractional calculus, they are now unavoidable tools for handling
various mathematical models of integer or fractional order. From
Bessel to Multi-Index Mittag-Leffler Functions analyzes this
through the study of enumerable families of different classes of
special functions.Enumerable families are considered and the
convergence of series is investigated. Providing a unified approach
to the classical power series, analogues of the classical results
for the power series are obtained, and the conclusion is that each
of the considered series has a similar convergence behavior to a
power series. Also studied are various properties of the Bessel and
Mittag-Leffler functions and their generalizations, including
estimations, asymptotic formulae, fractional differentiation and
integration operators.
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