On Multivariate Fractional Taylor's and Cauchy' Mean Value Theorem (Journal of Mathematical Study, 2019)
In this paper, a generalized multivariate fractional Taylor's and Cauchy's mean value theorem of the kind$$f(x,y) = \sum\limits_{j = 0}^n {\frac{{{D^{jα }}f({x_{0,}}{y_0})}}{{Γ (jα + 1)}}} + R_n^α (ξ,η),\qquad\frac{{f(x,y) - \sum\limits_{j = 0}^n {\frac{{{D^{jα }}f({x_{0,}}{y_0})}}{{Γ (jα + 1)}}} }}{{g(x,y) - \sum\limits_{j = 0}^n {\frac{{{D^{jα }}g({x_{0,}}{y_0})}}{{Γ (jα + 1)}}} }} = \frac{{R_n^α (ξ ,η )}}{{T_n^α (ξ ,η )}},$$where $0
Keywords: Sequential Caputo fractional derivative; generalized Taylor's mean value theorem; generalized Taylor's formula; generalized Cauchy' mean value theorem; generalized Cauchy's formula.