New insight in fractional differentiation: power, exponential decay and Mittag-Leffler laws and applications

. Some physical problems found in nature can follow the power law; others can follow the Mittag-Leffler law and others the exponential decay law. On the other hand, one can observe in nature a physical problem that combines the three laws, it is therefore important to provide a new fractional operat...

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Bibliographic Details
Published inEuropean physical journal plus Vol. 132; no. 1; p. 13
Main Authors Gómez-Aguilar, J. F., Atangana, Abdon
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2017
Springer Nature B.V
Subjects
Applied and Technical Physics
Atomic
Calculus
Complex Systems
Condensed Matter Physics
Decay
Mathematical and Computational Physics
Mathematical functions
Molecular
Operators (mathematics)
Optical and Plasma Physics
Physics
Physics and Astronomy
Power
Power law
Regular Article
Theoretical
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Summary:. Some physical problems found in nature can follow the power law; others can follow the Mittag-Leffler law and others the exponential decay law. On the other hand, one can observe in nature a physical problem that combines the three laws, it is therefore important to provide a new fractional operator that could possibly be used to model such physical problem. In this paper, we suggest a fractional operator power-law-exponential-Mittag-Leffler kernel with three fractional orders. Some very useful properties are obtained. Numerical solutions were obtained for three examples proposed. The results show that the new fractional operators are powerful mathematical tools to model complex problems.
ISSN:2190-5444
2190-5444
DOI:10.1140/epjp/i2017-11293-3