Some New Extensions on Fractional Differential and Integral Properties for Mittag-Leffler Confluent Hypergeometric Function

This article uses fractional calculus to create novel links between the well-known Mittag-Leffler functions of one, two, three, and four parameters. Hence, this paper studies several new analytical properties using fractional integration and differentiation for the Mittag-Leffler function formulated...

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Bibliographic Details
Published in:Fractal and fractional 2021-12, Vol.5 (4), p.143
Main Authors: Ghanim, F., Al-Janaby, Hiba F., Bazighifan, Omar
Format: Article
Language:English
Subjects:
Calculus
confluent hypergeometric function
Fractional calculus
Hypergeometric functions
Integral equations
integral operator
Integrals
laplace transform
Laplace transforms
Mathematical analysis
mittag-leffler function
Parameters
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Summary:This article uses fractional calculus to create novel links between the well-known Mittag-Leffler functions of one, two, three, and four parameters. Hence, this paper studies several new analytical properties using fractional integration and differentiation for the Mittag-Leffler function formulated by confluent hypergeometric functions. We construct a four-parameter integral expression in terms of one-parameter. The paper explains the significance and applications of each of the four Mittag-Leffler functions, with the goal of using our findings to make analyzing specific kinds of experimental results considerably simpler.
ISSN:2504-3110
2504-3110
DOI:10.3390/fractalfract5040143