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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.
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]
Copyright of Journal of Applied Mathematics is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Label: Title
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  Data: Existence and Uniqueness of Solutions to Initial Value Problems of High‐Order Fractional Fuzzy Differential Equations.
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  Data: <searchLink fieldCode="AR" term="%22Xi%2C+Yanli%22">Xi, Yanli</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> xyl9702@163.com</i><br /><searchLink fieldCode="AR" term="%22Bao%2C+Wenbin%22">Bao, Wenbin</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Habib%2C+Mohammad+Rezwan%22">Habib, Mohammad Rezwan</searchLink> (AUTHOR)<i> mohabib@wiley.com</i>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Applied+Mathematics%22">Journal of Applied Mathematics</searchLink>. 6/20/2026, Vol. 2026, p1-11. 11p.
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  Data: <searchLink fieldCode="DE" term="%22Fractional+differential+equations%22">Fractional differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Initial+value+problems%22">Initial value problems</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+systems%22">Nonlinear systems</searchLink><br /><searchLink fieldCode="DE" term="%22Uniqueness+%28Mathematics%29%22">Uniqueness (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Integral+operators%22">Integral operators</searchLink><br /><searchLink fieldCode="DE" term="%22Contraction+operators%22">Contraction operators</searchLink><br /><searchLink fieldCode="DE" term="%22Caputo+fractional+derivatives%22">Caputo fractional derivatives</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: 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]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Applied Mathematics is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1155/jama/3733765
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 11
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      – SubjectFull: Fractional differential equations
        Type: general
      – SubjectFull: Initial value problems
        Type: general
      – SubjectFull: Nonlinear systems
        Type: general
      – SubjectFull: Uniqueness (Mathematics)
        Type: general
      – SubjectFull: Integral operators
        Type: general
      – SubjectFull: Contraction operators
        Type: general
      – SubjectFull: Caputo fractional derivatives
        Type: general
    Titles:
      – TitleFull: Existence and Uniqueness of Solutions to Initial Value Problems of High‐Order Fractional Fuzzy Differential Equations.
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            NameFull: Xi, Yanli
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            NameFull: Bao, Wenbin
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            NameFull: Habib, Mohammad Rezwan
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            – D: 20
              M: 06
              Text: 6/20/2026
              Type: published
              Y: 2026
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              Value: 2026
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