N‐Dimensional Fractional Lagrange′s Inversion Theorem

F. A. Abd El-Salam

Abstract and Applied Analysis, 2013, vol. 2013, issue 1

Abstract: 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.

Date: 2013
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https://doi.org/10.1155/2013/310679

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:310679

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