Existence and Uniqueness of Solutions to Initial Value Problems of High‐Order Fractional Fuzzy Differential Equations.
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| Title: | Existence and Uniqueness of Solutions to Initial Value Problems of High‐Order Fractional Fuzzy Differential Equations. |
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| Authors: | Xi, Yanli1,2 (AUTHOR) xyl9702@163.com, Bao, Wenbin1 (AUTHOR), Habib, Mohammad Rezwan (AUTHOR) mohabib@wiley.com |
| Source: | Journal of Applied Mathematics. 6/20/2026, Vol. 2026, p1-11. 11p. |
| Subjects: | Fractional differential equations, Initial value problems, Nonlinear systems, Uniqueness (Mathematics), Integral operators, Contraction operators, Caputo fractional derivatives |
| Abstract: | High‐order fractional fuzzy differential equations show great potential in modeling complex systems with memory effects and uncertainty. Existing qualitative theories seldom involve both Caputo‐type strongly generalized Hukuhara differentiability and coupled integral operators on infinite intervals. This paper presents a systematic investigation of the initial value problem for a class of high‐order nonlinear fractional fuzzy differential equations involving parameters and double integral operators. By decomposing the problem into four typical cases of GH‐differentiability, and combining the method of successive approximations with the Banach contraction mapping principle in complete metric spaces, the existence and uniqueness of both local and global solutions to the problem are rigorously established. Furthermore, by employing inequality techniques, the continuous dependence of solutions on initial conditions is demonstrated, thereby verifying the well‐posedness of the problem. Finally, two illustrative examples are provided to demonstrate our new results. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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| Abstract: | High‐order fractional fuzzy differential equations show great potential in modeling complex systems with memory effects and uncertainty. Existing qualitative theories seldom involve both Caputo‐type strongly generalized Hukuhara differentiability and coupled integral operators on infinite intervals. This paper presents a systematic investigation of the initial value problem for a class of high‐order nonlinear fractional fuzzy differential equations involving parameters and double integral operators. By decomposing the problem into four typical cases of GH‐differentiability, and combining the method of successive approximations with the Banach contraction mapping principle in complete metric spaces, the existence and uniqueness of both local and global solutions to the problem are rigorously established. Furthermore, by employing inequality techniques, the continuous dependence of solutions on initial conditions is demonstrated, thereby verifying the well‐posedness of the problem. Finally, two illustrative examples are provided to demonstrate our new results. [ABSTRACT FROM AUTHOR] |
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| ISSN: | 1110757X |
| DOI: | 10.1155/jama/3733765 |
