Open AccessOn coupled Gronwall inequalities involving a $ \psi $-fractional integral operator with its applications
Author(s) -
Dinghong Jiang,
AUTHOR_ID,
Chuanzhi Bai,
AUTHOR_ID
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022434
Subject(s) - gronwall's inequality , uniqueness , mathematics , stability (learning theory) , operator (biology) , function (biology) , fractional calculus , nonlinear system , differential (mechanical device) , mathematical analysis , inequality , computer science , physics , biochemistry , chemistry , repressor , quantum mechanics , machine learning , evolutionary biology , biology , transcription factor , gene , thermodynamics
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.