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Lan, Kunquan

Linear first order Riemann-Liouville fractional differential and perturbed Abel’s integral equations. (English) Zbl 1490.34007

J. Differ. Equations 306, 28-59 (2022); corrigendum ibid. 345, 519-520 (2023).
The paper is concerned with linear first order Riemann-Liouville fractional differential equations which generalise several established classes of fractional differential equation. The fractional differential equations are shown to be equivalent to perturbed Abel integral equations. This is followed by two sections where the different forms of the problems are analysed: first the solutions of the Riemann-Liouville fractional differential equations and then the perturbed Abel integral equations.
The key conclusions of the paper include:
●
nonconstant equilibria exist for some first order Caputo fractional equations
●
a mean value theorem is provided for fractional derivatives
Reviewer: Neville Ford (Chester)

Cited in 1 Review
Cited in 5 Documents

MSC:

34A08 Fractional ordinary differential equations
26A33 Fractional derivatives and integrals
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
45D05 Volterra integral equations

Keywords:

Riemann-Liouville fractional differential equations; perturbed Abel integral equation; mean value theorems for fractional derivatives; equivalence

Software:

DFOC; sysdfod
PDFBibTeX XMLCite
\textit{K. Lan}, J. Differ. Equations 306, 28--59 (2022; Zbl 1490.34007)
Full Text: DOI

References:

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