Fuzzy fractional delay integro-differential equation with the generalized Atangana-Baleanu fractional derivative

• Published in: Demonstratio mathematica Vol. 57; no. 1; pp. 229 - 48
• Main Authors: Wang, Guotao, Feng, Meihua, Zhao, Xianghong, Yuan, Hualei
• Format: Journal Article
• Language: English
• Published: De Gruyter 23.07.2024
• Subjects: 26A33; 34A08; fuzzy fractional delay integro-differential equation; generalized Atangana-Baleanu fractional derivative; Monotone iterative method
• ISSN: 2391-4661; 2391-4661
• DOI: 10.1515/dema-2024-0008

In this work, we consider a class of fuzzy fractional delay integro-differential equations with the generalized Caputo-type Atangana-Baleanu (ABC) fractional derivative. By using the monotone iterative method, we not only obtain the existence and uniqueness of the solution for the given problem with the initial condition but also give the monotone iteration sequence converging to the unique solution of the problem. Furthermore, we also give the continuous dependence of the unique solution on initial value. Finally, an example is presented to illustrate the main results obtained. The results presented in this study are new and open a new avenue of research for fuzzy fractional delay integro-differential equations with the generalized ABC fractional derivative.