Existence Criteria for the Unique Solution of First Order Linear Fuzzy Differential Equations on the Space of Linearly Correlated Fuzzy Numbers

Abstract

This study is concerned with the existence and uniqueness results for fuzzy differential equations (FDEs). The existence result of FDEs in the space of linear correlated (LC) fuzzy number with LC-differentiability is the goal of this work. Linear FDEs of first order in the space of LC-fuzzy number mostly have many solutions and sometimes have no solutions. Existence theory insures the existence of unique solution of FDEs. Therefore, we propose to study the existence results of LC-fuzzy solution of FDEs of first order. The existence criteria for the unique LC-fuzzy solution for both symmetric and nonsymmetric basic fuzzy number will be studied in this work. Some examples are given to show the usability of the criteria for a unique LC-fuzzy solution. The plots of the fuzzy solutions of examples are also provided.

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