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 |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 2314-8888 |