Abstract
In this work, we use the fuzzy strongly continuous semigroup theory to prove the existence, uniqueness, and some properties of solutions of fuzzy differential equations with nonlocal conditions.
Highlights
We prove the existence and uniqueness of mild solutions for the following fuzzy differential equations with nonlocal conditions:
In Section, we study the continuous dependence between mild solutions and initial data
All authors read and approved the final manuscript
Summary
Balachandran and Chandrasekaran [ ] proved the existence and uniqueness of the solutions of a fuzzy delay differential equation with nonlocal conditions. Balasubramaniam and Muralisankar [ ] studied the neutral problem d dt x(t) – f (t, xt) = Ax(t) + g(t, xt), x(t) = ψ(t), on J = [ , T], where f , g : J × En → En are fuzzy level-wise continuous functions, and A is a fuzzy coefficient. We prove the existence and uniqueness of mild solutions for the following fuzzy differential equations with nonlocal conditions:. In Section , we give sufficient conditions for the existence and uniqueness of a mild solution of the fuzzy differential equation with nonlocal condition ( ). The last section is devoted to a study of a particular case
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