On the existence of generalized weak solutions to discontinuous fuzzy differential equations


Authors

Ya-Bin Shao - School of Science, Chongqing University of Posts and Telecommunications, 400065 Nanan, Chongqing, People's Republic of China. Zeng-Tai Gong - College of Mathematics and Statistics, Northwest Normal University, 730070 Lanzhou, Gansu, People's Republic of China. Zi-Zhong Chen - College of Computer Science and Technology, Chongqing University of Posts and Telecommunications, 400065 Nanan, Chongqing, People's Republic of China.


Abstract

In this paper, by means of replacing the Lebesgue integrability of support functions with its Henstock integrability, the definitions of the Henstock-Pettis integral of \(n\)-dimensional fuzzy-number-valued functions are defined. In addition, the controlled convergence theorems for such integrals are considered. As the applications of these integrals, we provide some existence theorems of generalized weak solutions to initial value problems for the discontinuous fuzzy differential equations under the strong GH-differentiability.


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ISRP Style

Ya-Bin Shao, Zeng-Tai Gong, Zi-Zhong Chen, On the existence of generalized weak solutions to discontinuous fuzzy differential equations, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 12, 6274--6287

AMA Style

Shao Ya-Bin, Gong Zeng-Tai, Chen Zi-Zhong, On the existence of generalized weak solutions to discontinuous fuzzy differential equations. J. Nonlinear Sci. Appl. (2017); 10(12):6274--6287

Chicago/Turabian Style

Shao, Ya-Bin, Gong, Zeng-Tai, Chen, Zi-Zhong. "On the existence of generalized weak solutions to discontinuous fuzzy differential equations." Journal of Nonlinear Sciences and Applications, 10, no. 12 (2017): 6274--6287


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