Finite-time stability of Caputo fractional fuzzy differential equations with delay in granular sense

This manuscript focuses on investigating a class of Caputo fractional fuzzy differential system with time delay. Firstly, we understand the granular form of fuzzy numbers from a novel perspective, which contains more information than the usual membership function. Subsequently, using a successive approximation approach under the granular arithmetic context, we demonstrate the existence of the solution to this system, and the uniqueness is obtained by the completeness of fuzzy space. Furthermore, we establish a criterion for determining the finite-time stability of the system, and which is an evaluation function containing optional parameter ζ∈(0,ν) by employing a Gronwall inequality with delay form, where ν is the order of the Caputo derivative. Finally, we present a numerical example to verify our primary findings and discuss the appropriate selection of parameter ζ to optimize the evaluation function.