N-Dimensional Fractional Lagrange's Inversion Theorem

Abstract EN

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.