-Dimensional Fractional Lagrange's Inversion Theorem
Keyword(s):
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 -dimensional polyadics is derived. A fractional -dimensional Lagrange inversion theorem is proved.
2015 ◽
Vol 11
(1)
◽
pp. 19-32
2018 ◽
Vol 505
◽
pp. 688-706
◽
2020 ◽
Vol 23
(2)
◽
pp. 553-570
◽
2013 ◽
Vol 2013
◽
pp. 1-3
◽