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<p>Fractional power series in several variables are investigated within the framework of fractional calculus. By employing the Riemann-Liouville fractional integral and Caputo derivative, a generalized Taylor’s formula for multivariable functions is established, extending previously known results for the single-variable case. A sufficient condition for representing a multivariable function as a fractional power series is stated and a framework for obtaining approximate solutions of fractional partial differential equations is provided. In addition, the paper presents a method for determining restricted local extrema of multivariable functions. Illustrative examples are included.</p>

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Multivariable functions represented as fractional power series and generalized Taylor’s formula

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月29日

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  • Ghiocel Groza,
  • Marilena Jianu

摘要

Fractional power series in several variables are investigated within the framework of fractional calculus. By employing the Riemann-Liouville fractional integral and Caputo derivative, a generalized Taylor’s formula for multivariable functions is established, extending previously known results for the single-variable case. A sufficient condition for representing a multivariable function as a fractional power series is stated and a framework for obtaining approximate solutions of fractional partial differential equations is provided. In addition, the paper presents a method for determining restricted local extrema of multivariable functions. Illustrative examples are included.