Existence and Uniqueness of Mild Solution for Fractional-Order Controlled Fuzzy Evolution Equation
In this article, we investigated the existence and uniqueness of mild solutions for fractional-order controlled fuzzy evolution equations with Caputo derivatives of the controlled fuzzy nonlinear evolution equation of the form 0cDIγxI=αxI+PI,xI+AIWI,I∈0,T,xI0=x0, in which γ∈0,1, E1 is the fuzzy met...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2021/5795065 |
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| _version_ | 1832566439797587968 |
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| author | Naveed Iqbal Azmat Ullah Khan Niazi Ramsha Shafqat Shamsullah Zaland |
| author_facet | Naveed Iqbal Azmat Ullah Khan Niazi Ramsha Shafqat Shamsullah Zaland |
| author_sort | Naveed Iqbal |
| collection | DOAJ |
| description | In this article, we investigated the existence and uniqueness of mild solutions for fractional-order controlled fuzzy evolution equations with Caputo derivatives of the controlled fuzzy nonlinear evolution equation of the form 0cDIγxI=αxI+PI,xI+AIWI,I∈0,T,xI0=x0, in which γ∈0,1, E1 is the fuzzy metric space and I=0,T is a real line interval. With the help of few conditions on functions P:I×E1×E1⟶E1, WI is control and it belongs to E1, A∈FI,LE1, and α stands for the highly continuous fuzzy differential equation generator. Finally, a few instances of fuzzy fractional differential equations are shown. |
| format | Article |
| id | doaj-art-cc066dc0c7ae441894075cbb5d0a3526 |
| institution | Kabale University |
| issn | 2314-8888 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-cc066dc0c7ae441894075cbb5d0a35262025-02-03T01:04:16ZengWileyJournal of Function Spaces2314-88882021-01-01202110.1155/2021/5795065Existence and Uniqueness of Mild Solution for Fractional-Order Controlled Fuzzy Evolution EquationNaveed Iqbal0Azmat Ullah Khan Niazi1Ramsha Shafqat2Shamsullah Zaland3Department of MathematicsFaculty of Mathematics and Computational ScienceDepartment of Mathematics and StatisticsFaculty of MathematicsIn this article, we investigated the existence and uniqueness of mild solutions for fractional-order controlled fuzzy evolution equations with Caputo derivatives of the controlled fuzzy nonlinear evolution equation of the form 0cDIγxI=αxI+PI,xI+AIWI,I∈0,T,xI0=x0, in which γ∈0,1, E1 is the fuzzy metric space and I=0,T is a real line interval. With the help of few conditions on functions P:I×E1×E1⟶E1, WI is control and it belongs to E1, A∈FI,LE1, and α stands for the highly continuous fuzzy differential equation generator. Finally, a few instances of fuzzy fractional differential equations are shown.http://dx.doi.org/10.1155/2021/5795065 |
| spellingShingle | Naveed Iqbal Azmat Ullah Khan Niazi Ramsha Shafqat Shamsullah Zaland Existence and Uniqueness of Mild Solution for Fractional-Order Controlled Fuzzy Evolution Equation Journal of Function Spaces |
| title | Existence and Uniqueness of Mild Solution for Fractional-Order Controlled Fuzzy Evolution Equation |
| title_full | Existence and Uniqueness of Mild Solution for Fractional-Order Controlled Fuzzy Evolution Equation |
| title_fullStr | Existence and Uniqueness of Mild Solution for Fractional-Order Controlled Fuzzy Evolution Equation |
| title_full_unstemmed | Existence and Uniqueness of Mild Solution for Fractional-Order Controlled Fuzzy Evolution Equation |
| title_short | Existence and Uniqueness of Mild Solution for Fractional-Order Controlled Fuzzy Evolution Equation |
| title_sort | existence and uniqueness of mild solution for fractional order controlled fuzzy evolution equation |
| url | http://dx.doi.org/10.1155/2021/5795065 |
| work_keys_str_mv | AT naveediqbal existenceanduniquenessofmildsolutionforfractionalordercontrolledfuzzyevolutionequation AT azmatullahkhanniazi existenceanduniquenessofmildsolutionforfractionalordercontrolledfuzzyevolutionequation AT ramshashafqat existenceanduniquenessofmildsolutionforfractionalordercontrolledfuzzyevolutionequation AT shamsullahzaland existenceanduniquenessofmildsolutionforfractionalordercontrolledfuzzyevolutionequation |