N-Dimensional Fractional Lagrange's Inversion Theorem

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...

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Bibliographic Details
Published in:Abstract and Applied Analysis 2013-01, Vol.2013, p.342-352-331
Main Author: F. A. Abd El-Salam
Format: Article
Language:English
Subjects:
Calculus
Independent variables
Inversions
Mathematical analysis
Operators
Tensors
Theorems
Vectors (mathematics)
Online Access:Get full text
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Summary: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.
ISSN:1085-3375
1687-0409
DOI:10.1155/2013/310679