# Continuous solutions to a class of first-order fuzzy differential equations with discontinuous coefficients

## Abstract

In this paper, we study the continuity of solution functions to a class of fuzzy differential equations (FDEs) in the form \(y'(t)=\frac{\varphi (t)}{(t-\alpha )^{p}}\odot y(t)+\psi (t)\), where the coefficient function \(\frac{\varphi (t)}{(t-\alpha )^{p}}\) is a discontinuous function at the point \(t=\alpha \) and \(\alpha \) is an inner point of the interval under study. At first, the continuity of solutions for the crisp case of the problem is investigated and those results are extended to the fuzzy case of the problem from the view point of strongly generalized differentiability (G-differentiability). Next, we obtain explicit formulas of solutions and the conditions of their existence for a special class of these problems. Finally, the results are illustrated by solving some examples.

## Keywords

Fuzzy differential equations Generalized differentiability Fuzzy-valued functions Continuous solutions## Mathematics Subject Classification

34A07 34K36 08A72 03E72 93C42 90C70## References

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