On fuzzy Laplace transform in linearly correlated fuzzy space

In this manuscript, we present the notion of improper Riemann integral and develop a methodology to solve nth-order fuzzy initial value problems (FIVPs) via fuzzy Laplace transform for linearly correlated processes. Our approach translates a fuzzy differential equation (FDE) problem from the fuzzy number space to a well-established Banach space. In this new approach, it is not necessary to consider several cases due to switch points, and we do not need to use the Stacking theorem because the obtained solution is always a fuzzy number. In order to illustrate our approach, we present several examples comparing the obtained solutions with those produced by other methods.