Rocky Mountain Journal of Mathematics

Further properties of Osler's generalized fractional integrals and derivatives with respect to another function

Ricardo Almeida

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Abstract

In this paper we discuss fractional integrals and fractional derivatives of a function with respect to another function. We present some fundamental properties for both types of fractional operators, such as Taylor's theorem, Leibniz and semigroup rules. We also provide a numerical tool to deal with these operators, by approximating them with a sum involving integer-order derivatives.

Article information

Source
Rocky Mountain J. Math., Volume 49, Number 8 (2019), 2459-2493.

Dates
First available in Project Euclid: 31 January 2020

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1580461777

Digital Object Identifier
doi:10.1216/RMJ-2019-49-8-2459

Mathematical Reviews number (MathSciNet)
MR4058333

Zentralblatt MATH identifier
07163182

Subjects
Primary: 26A33: Fractional derivatives and integrals 26A24: Differentiation (functions of one variable): general theory, generalized derivatives, mean-value theorems [See also 28A15] 41A58: Series expansions (e.g. Taylor, Lidstone series, but not Fourier series)

Keywords
Fractional integral fractional derivative Taylor's theorem semigroup law expansion formulas

Citation

Almeida, Ricardo. Further properties of Osler's generalized fractional integrals and derivatives with respect to another function. Rocky Mountain J. Math. 49 (2019), no. 8, 2459--2493. doi:10.1216/RMJ-2019-49-8-2459. https://projecteuclid.org/euclid.rmjm/1580461777


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