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June 2020 Exact solutions of linear Riemann–Liouville fractional differential equations with impulses
Ravi P. Agarwal, Snezhana Hristova, Donal O’Regan
Rocky Mountain J. Math. 50(3): 779-791 (June 2020). DOI: 10.1216/rmj.2020.50.779

Abstract

Linear Riemann–Liouville fractional differential equations with impulses are studied in the case of scalar equations and the case of systems. Both cases are considered: the case when the lower limit of the fractional derivative is fixed on the whole interval of consideration and the case when the lower limit of the fractional derivative is changed at any point of impulse. Two types of initial conditions and impulsive conditions are applied to set up initial value problems for fractional differential equations with impulses. Explicit formulas for the solutions are obtained. The Mittag-Leffler function and the matrix generalization of the fractional exponential function are applied.

Citation

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Ravi P. Agarwal. Snezhana Hristova. Donal O’Regan. "Exact solutions of linear Riemann–Liouville fractional differential equations with impulses." Rocky Mountain J. Math. 50 (3) 779 - 791, June 2020. https://doi.org/10.1216/rmj.2020.50.779

Information

Received: 1 August 2019; Revised: 3 December 2019; Accepted: 3 December 2019; Published: June 2020
First available in Project Euclid: 29 July 2020

zbMATH: 07235579
MathSciNet: MR4132609
Digital Object Identifier: 10.1216/rmj.2020.50.779

Subjects:
Primary: 34A08, 34A37

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.50 • No. 3 • June 2020
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