Existence, continuous dependence and finite time stability for Riemann-Liouville fractional differential equations with a constant delay

Snezhana Hristova; Antonia Dobreva; Snezhana Hristova; Antonia Dobreva

doi:10.3934/math.2020247

AIMS Mathematics

2020, Volume 5, Issue 4: 3809-3824. doi: 10.3934/math.2020247

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Research article

Existence, continuous dependence and finite time stability for Riemann-Liouville fractional differential equations with a constant delay

Snezhana Hristova ^,,
Antonia Dobreva

Department of Applied Mathematics and Modeling, University of Plovdiv “P. Hilendarski”, Plovdiv 4000, Bulgaria

Received: 24 November 2019 Accepted: 31 March 2020 Published: 21 April 2020
MSC : 34A08, 34A37

Non-linear scalar Riemann-Liouville fractional differential equation with a constant delay is studied on a finite interval. An initial value problem is set up in appropriate way combining the idea of the initial time interval in ordinary differential equations with delays and the properties of Riemann-Liouville fractional derivatives. The mild solution of the studied initial value problem is defined. The existence, uniqueness, continuous dependence on the initial functions, finite time stability of the mild solutions are investigated.
- Riemann-Liouville fractional derivative,
- constant delay,
- initial value problem,
- existence,
- finite time stability
Citation: Snezhana Hristova, Antonia Dobreva. Existence, continuous dependence and finite time stability for Riemann-Liouville fractional differential equations with a constant delay[J]. AIMS Mathematics, 2020, 5(4): 3809-3824. doi: 10.3934/math.2020247

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Abstract

Non-linear scalar Riemann-Liouville fractional differential equation with a constant delay is studied on a finite interval. An initial value problem is set up in appropriate way combining the idea of the initial time interval in ordinary differential equations with delays and the properties of Riemann-Liouville fractional derivatives. The mild solution of the studied initial value problem is defined. The existence, uniqueness, continuous dependence on the initial functions, finite time stability of the mild solutions are investigated.

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