Uncertainty distributions of solutions to nabla Caputo uncertain difference equations and application to a logistic model

Qinyun Lu; Ya Li; Hai Zhang; Hongmei Zhang; Qinyun Lu; Ya Li; Hai Zhang; Hongmei Zhang

doi:10.3934/math.20241154

AIMS Mathematics

2024, Volume 9, Issue 9: 23752-23769. doi: 10.3934/math.20241154

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Research article

Uncertainty distributions of solutions to nabla Caputo uncertain difference equations and application to a logistic model

School of Mathematics and Physics, Anqing Normal University, Anqing 246133, China

Received: 28 May 2024 Revised: 22 July 2024 Accepted: 26 July 2024 Published: 08 August 2024
MSC : 39A13, 92D25

The nabla fractional-order uncertain difference equation with Caputo-type was analyzed in this article. To begin, the existence and uniqueness theorem of solutions for nabla Caputo uncertain difference equations with almost surely bounded uncertain variables was presented. Furthermore, the uncertainty distributions of the solutions for the proposed equations were obtained by establishing a connection between the solutions of equations and their $ \alpha $-paths based on new comparison theorems. Finally, an application of the uncertain difference equations in a logistic population model involving Allee effect was provided and examples were performed to demonstrate the validity of the theoretical results presented.
- uncertainty distribution,
- $ \alpha $-paths,
- nabla difference,
- fractional-order difference equation,
- logistic model
Citation: Qinyun Lu, Ya Li, Hai Zhang, Hongmei Zhang. Uncertainty distributions of solutions to nabla Caputo uncertain difference equations and application to a logistic model[J]. AIMS Mathematics, 2024, 9(9): 23752-23769. doi: 10.3934/math.20241154

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Abstract

The nabla fractional-order uncertain difference equation with Caputo-type was analyzed in this article. To begin, the existence and uniqueness theorem of solutions for nabla Caputo uncertain difference equations with almost surely bounded uncertain variables was presented. Furthermore, the uncertainty distributions of the solutions for the proposed equations were obtained by establishing a connection between the solutions of equations and their $ \alpha $-paths based on new comparison theorems. Finally, an application of the uncertain difference equations in a logistic population model involving Allee effect was provided and examples were performed to demonstrate the validity of the theoretical results presented.

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