2021 Weighted Cauchy problem: fractional versus integer order
María Guadalupe Morales, Zuzana Došlá
J. Integral Equations Applications 33(4): 497-509 (2021). DOI: 10.1216/jie.2021.33.497

Abstract

This work is devoted to the solvability of the weighted Cauchy problem for fractional differential equations of arbitrary order, considering the Riemann–Liouville derivative. We show the equivalence between the weighted Cauchy problem and the Volterra integral equation in the space of Lebesgue integrable functions. Finally, we point out some discrepancies between the solutions for fractional and integer order case.

Citation

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María Guadalupe Morales. Zuzana Došlá. "Weighted Cauchy problem: fractional versus integer order." J. Integral Equations Applications 33 (4) 497 - 509, 2021. https://doi.org/10.1216/jie.2021.33.497

Information

Received: 5 May 2020; Accepted: 15 June 2021; Published: 2021
First available in Project Euclid: 11 March 2022

MathSciNet: MR4393381
zbMATH: 1510.34021
Digital Object Identifier: 10.1216/jie.2021.33.497

Subjects:
Primary: 26A33 , 34A12 , 45D05

Keywords: Fractional differential equations , Lipschitz operator , Riemann–Liouville fractional derivative , unweighted Cauchy problem , Volterra integral equation , weighted Cauchy problem

Rights: Copyright © 2021 Rocky Mountain Mathematics Consortium

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Vol.33 • No. 4 • 2021
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