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February 2022 Existence and stability results on multidimensional fractional-order systems
Arzu Ahmadova, Ismail T. Huseynov, Nazim I. Mahmudov
Rocky Mountain J. Math. 52(1): 1-14 (February 2022). DOI: 10.1216/rmj.2022.52.1

Abstract

The novelties of this paper is the study of existence and uniqueness results for a class of incommensurate fractional differential equation systems with general multiorders using the weighted infinity norm with respect to the classical Mittag-Leffler function via the contraction mapping principle. The lack of stability results in the Ulam–Hyers sense on fractional multidimensional differential equations motivates us to generalize our theory to stability analysis based on fixed point approach.

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Arzu Ahmadova. Ismail T. Huseynov. Nazim I. Mahmudov. "Existence and stability results on multidimensional fractional-order systems." Rocky Mountain J. Math. 52 (1) 1 - 14, February 2022. https://doi.org/10.1216/rmj.2022.52.1

Information

Received: 10 November 2020; Revised: 5 June 2021; Accepted: 18 June 2021; Published: February 2022
First available in Project Euclid: 19 April 2022

Digital Object Identifier: 10.1216/rmj.2022.52.1

Subjects:
Primary: 34A08 , 34A12

Keywords: Caputo fractional derivative , existence and uniqueness , incommensurate fractional-order system , Mittag–Leffler functions , multidimensional fractional differential equations system , Ulam–Hyers stability

Rights: Copyright © 2022 Rocky Mountain Mathematics Consortium

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Vol.52 • No. 1 • February 2022
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