Some Properties of the Functions Representable as Fractional Power Series

Ghiocel Groza, Marilena Jianu () and Ion Mierluş-Mazilu
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Ghiocel Groza: Department of Mathematics and Computer Science, Technical University of Civil Engineering Bucharest, Bd. Lacul Tei 124, Sector 2, 38RO-020396 Bucharest, Romania
Marilena Jianu: Department of Mathematics and Computer Science, Technical University of Civil Engineering Bucharest, Bd. Lacul Tei 124, Sector 2, 38RO-020396 Bucharest, Romania
Ion Mierluş-Mazilu: Department of Mathematics and Computer Science, Technical University of Civil Engineering Bucharest, Bd. Lacul Tei 124, Sector 2, 38RO-020396 Bucharest, Romania

Mathematics, 2024, vol. 12, issue 7, 1-13

Abstract: The α -fractional power moduli series are introduced as a generalization of α -fractional power series and the structural properties of these series are investigated. Using the fractional Taylor’s formula, sufficient conditions for a function to be represented as an α -fractional power moduli series are established. Beyond theoretical formulations, a practical method to represent solutions to boundary value problems for fractional differential equations as α -fractional power series is discussed. Finally, α -analytic functions on an open interval I are defined, and it is shown that a non-constant function is α -analytic on I if and only if 1 / α is a positive integer and the function is real analytic on I .

Keywords: Caputo fractional derivative operator; fractional power series; fractional analytic function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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