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2013 N -Dimensional Fractional Lagrange's Inversion Theorem
F. A. Abd El-Salam
Abstr. Appl. Anal. 2013: 1-11 (2013). DOI: 10.1155/2013/310679


Using Riemann-Liouville fractional differential operator, a fractional extension of the Lagrange inversion theorem and related formulas are developed. The required basic definitions, lemmas, and theorems in the fractional calculus are presented. A fractional form of Lagrange's expansion for one implicitly defined independent variable is obtained. Then, a fractional version of Lagrange's expansion in more than one unknown function is generalized. For extending the treatment in higher dimensions, some relevant vectors and tensors definitions and notations are presented. A fractional Taylor expansion of a function of N -dimensional polyadics is derived. A fractional N -dimensional Lagrange inversion theorem is proved.


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F. A. Abd El-Salam. " N -Dimensional Fractional Lagrange's Inversion Theorem." Abstr. Appl. Anal. 2013 1 - 11, 2013.


Published: 2013
First available in Project Euclid: 27 February 2014

zbMATH: 1275.44002
MathSciNet: MR3035383
Digital Object Identifier: 10.1155/2013/310679

Rights: Copyright © 2013 Hindawi

Vol.2013 • 2013
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