Journal
ABSTRACT AND APPLIED ANALYSIS
Volume -, Issue -, Pages -Publisher
HINDAWI LTD
DOI: 10.1155/2013/310679
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- [3017/1434]
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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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