Quantitative analysis and stability results in $  \beta $-normed space for sequential differential equations with variable coefficients involving two fractional derivatives

Debao Yan; Debao Yan

doi:10.3934/math.20241690

AIMS Mathematics

2024, Volume 9, Issue 12: 35626-35644. doi: 10.3934/math.20241690

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Research article

Quantitative analysis and stability results in $ \beta $-normed space for sequential differential equations with variable coefficients involving two fractional derivatives

Debao Yan ^,

School of Mathematics and Statistics, Heze University, Heze City, Shandong Province, 274000, China

Received: 13 October 2024 Revised: 24 November 2024 Accepted: 11 December 2024 Published: 23 December 2024
MSC : 34A08, 34B10, 34B15, 34D20

This article conducted an analysis on quantitative properties and stability in a $ \beta $-normed space for a category of boundary value problems of nonlinear two-term fractional-order sequential differential equations with variable coefficients. The original problem was converted into an equivalent integral equation. Banach's fixed-point principle and Shaefer's fixed-point theorem were exploited to ensure that two existence conditions of the solutions for the problems were established. In addition, the stability known as $ \beta $-Ulam-Hyers for such problems has also been analyzed. Illustrative examples demonstrated practical applications of the work.
- quantitative analysis,
- sequential fractional differential equations,
- variable coefficients,
- $ \beta $-Ulam-Hyers stability
Citation: Debao Yan. Quantitative analysis and stability results in $ \beta $-normed space for sequential differential equations with variable coefficients involving two fractional derivatives[J]. AIMS Mathematics, 2024, 9(12): 35626-35644. doi: 10.3934/math.20241690

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Abstract

This article conducted an analysis on quantitative properties and stability in a $ \beta $-normed space for a category of boundary value problems of nonlinear two-term fractional-order sequential differential equations with variable coefficients. The original problem was converted into an equivalent integral equation. Banach's fixed-point principle and Shaefer's fixed-point theorem were exploited to ensure that two existence conditions of the solutions for the problems were established. In addition, the stability known as $ \beta $-Ulam-Hyers for such problems has also been analyzed. Illustrative examples demonstrated practical applications of the work.

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