University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 23 4 2026 08 01 The explicit solution to fuzzy differential equation with piecewise constant arguments involving the multi-order fractional derivative in (1,2) 183 201 10040 10.22111/ijfs.2026.54660.9681 EN Van Phut Lai Department of Mathematics, FPT University HCM, Saigon Hi-tech Park, Ho Chi Minh City, Vietnam Van Hoa Ngo Laboratory for Applied and Industrial Mathematics, Institute for Computational Science and Artificial Intelligence, Van Lang University, Ho Chi Minh City, Vietnam Journal Article 2026 02 05 This paper investigates non-homogeneous linear fuzzy fractional differential equations with piecewise constant arguments involving generalized multi-order Caputo fractional derivatives of order $\mathfrak{q}_{\imath} \in (1,2)$. By employing generalized single-level constrained fuzzy arithmetic, explicit closed-form solutions are obtained. A fuzzy vehicle-following model is included to demonstrate the applicability of the proposed results and to illustrate the effects of fractional orders, kernel functions, and fuzzy disturbances on the solution behavior. Fuzzy non-homogeneous linear differential equations piecewise constant arguments generalized multi-order Caputo fractional derivative explicit solution variation of constants formula https://ijfs.usb.ac.ir/article_10040_f06b726fcaa58b0597cba0b34972f3dc.pdf