Existence theorems for solutions to random fuzzy differential equations (Q988799)

The author considers random fuzzy differential equations (RFDEs) as models for the dynamics of real phenomena which are subject to two kinds of uncertainties: randomness and fuzziness, simultaneously. He examines RFDEs with two kinds of fuzzy derivatives and obtains parallel results for both settings. Supposing that the Lipschitz condition holds on bounded sets, the author establishes the existence and uniqueness of a local solution to RFDEs. The existence of at least one local solution is obtained under the assumption that the right-hand side of the equation satisfies some integrability condition. Also the author presents some examples which illustrate the theory of RFDEs.