On coupled Gronwall inequalities involving a $ \psi $-fractional integral operator with its applications

Dinghong Jiang; Chuanzhi Bai; Dinghong Jiang; Chuanzhi Bai

doi:10.3934/math.2022434

AIMS Mathematics

2022, Volume 7, Issue 5: 7728-7741. doi: 10.3934/math.2022434

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Research article

On coupled Gronwall inequalities involving a $ \psi $-fractional integral operator with its applications

Dinghong Jiang ^1,2,
Chuanzhi Bai ^{1
,
,}

1.
Department of Mathematics, Huaiyin Normal University, Huaian, Jiangsu 223300, China
2.
Huaiyin High School in Jiangsu Province, Huaian, Jiangsu 223002, China

Received: 18 November 2021 Revised: 12 February 2022 Accepted: 14 February 2022 Published: 17 February 2022
MSC : 26A24, 26A33, 26D10, 34A08, 34D20, 35A23, 39B82, 47H10

In this paper, we obtain a new generalized coupled Gronwall inequality through the Caputo fractional integral with respect to another function $ \psi $. Based on this result, we prove the existence and uniqueness of solutions for nonlinear delay coupled $ \psi $-Caputo fractional differential system. Moreover, the Ulam-Hyers stability of solutions for $ \psi $-Caputo fractional differential system is discussed. An example is also presented to demonstrate the application of main results.
Citation: Dinghong Jiang, Chuanzhi Bai. On coupled Gronwall inequalities involving a $ \psi $-fractional integral operator with its applications[J]. AIMS Mathematics, 2022, 7(5): 7728-7741. doi: 10.3934/math.2022434

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Abstract

In this paper, we obtain a new generalized coupled Gronwall inequality through the Caputo fractional integral with respect to another function $ \psi $. Based on this result, we prove the existence and uniqueness of solutions for nonlinear delay coupled $ \psi $-Caputo fractional differential system. Moreover, the Ulam-Hyers stability of solutions for $ \psi $-Caputo fractional differential system is discussed. An example is also presented to demonstrate the application of main results.

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