Asymptotic solutions of fractional interval differential equations with nonsingular kernel derivative.

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ID: 30304
2019
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Abstract
Realizing the behavior of the solution in the asymptotic situations is essential for repetitive applications in the control theory and modeling of the real-world systems. This study discusses a robust and definitive attitude to find the interval approximate asymptotic solutions of fractional differential equations (FDEs) with the Atangana-Baleanu (A-B) derivative. In fact, such critical tasks require to observe precisely the behavior of the noninterval case at first. In this regard, we initially shed light on the noninterval cases and analyze the behavior of the approximate asymptotic solutions, and then, we introduce the A-B derivative for FDEs under interval arithmetic and develop a new and reliable approximation approach for fractional interval differential equations with the interval A-B derivative to get the interval approximate asymptotic solutions. We exploit Laplace transforms to get the asymptotic approximate solution based on the interval asymptotic A-B fractional derivatives under interval arithmetic. The techniques developed here provide essential tools for finding interval approximation asymptotic solutions under interval fractional derivatives with nonsingular Mittag-Leffler kernels. Two cases arising in the real-world systems are modeled under interval notion and given to interpret the behavior of the interval approximate asymptotic solutions under different conditions as well as to validate this new approach. This study highlights the importance of the asymptotic solutions for FDEs regardless of interval or noninterval parameters.
Reference Key
salahshour2019asymptoticchaos Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Salahshour, S;Ahmadian, A;Salimi, M;Ferrara, M;Baleanu, D;
Journal chaos (woodbury, ny)
Year 2019
DOI
10.1063/1.5096022
URL
Keywords Keywords not found

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