Existence of solutions for a class of fractional dynamical systems with two damping terms in Banach space

Shuli Zhang; Yansheng Liu; Shuli Zhang; Yansheng Liu

doi:10.3934/mmc.2023015

Mathematical Modelling and Control

2023, Volume 3, Issue 3: 168-180. doi: 10.3934/mmc.2023015

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Existence of solutions for a class of fractional dynamical systems with two damping terms in Banach space

Shuli Zhang ,
Yansheng Liu ^,

School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China

Received: 01 December 2022 Revised: 15 February 2023 Accepted: 05 March 2023 Published: 31 August 2023

This paper studies the existence of solutions for fractional dynamical systems with two damping terms in Banach space. First, we generalize the well-known Gronwall inequality. Next, according to fixed-point theorems and inequalities, the existence results for the considered system are obtained. At last, an example is used to support the main results.
- Gronwall inequality,
- fixed point theorems,
- fractional differential equation,
- two damping terms
Citation: Shuli Zhang, Yansheng Liu. Existence of solutions for a class of fractional dynamical systems with two damping terms in Banach space[J]. Mathematical Modelling and Control, 2023, 3(3): 168-180. doi: 10.3934/mmc.2023015

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Abstract

This paper studies the existence of solutions for fractional dynamical systems with two damping terms in Banach space. First, we generalize the well-known Gronwall inequality. Next, according to fixed-point theorems and inequalities, the existence results for the considered system are obtained. At last, an example is used to support the main results.

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