Geometrical explanation of the fractional complex transform and derivative chain rule for fractional calculus

The fractional complex transform is suggested to convert a fractional differential equation with Jumarieʼs modification of Riemann–Liouville derivative into its classical differential partner. Understanding the fractional complex transform and the chain rule for fractional calculus are elucidated ge...

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Bibliographic Details
Published in:Physics letters. A 2012-01, Vol.376 (4), p.257-259
Main Authors: He, Ji-Huan, Elagan, S.K., Li, Z.B.
Format: Article
Language:English
Subjects:
Chain rule for fractional calculus
Fractional complex transform
Modified Riemann–Liouville derivative
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Summary:The fractional complex transform is suggested to convert a fractional differential equation with Jumarieʼs modification of Riemann–Liouville derivative into its classical differential partner. Understanding the fractional complex transform and the chain rule for fractional calculus are elucidated geometrically. ► The chain rule for fractional calculus is invalid, a counter example is given. ► The fractional complex transform is explained geometrically. ► Fractional equations can be converted into differential equations.
ISSN:0375-9601
1873-2429
DOI:10.1016/j.physleta.2011.11.030