The explicit solution to fuzzy differential equation with piecewise constant arguments involving the multi-order fractional derivative in (1,2)

Document Type : Research Paper

Authors

1 Department of Mathematics, FPT University HCM, Saigon Hi-tech Park, Ho Chi Minh City, Vietnam

2 Laboratory for Applied and Industrial Mathematics, Institute for Computational Science and Artificial Intelligence, Van Lang University, Ho Chi Minh City, Vietnam

10.22111/ijfs.2026.54660.9681

Abstract

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.

Keywords

Main Subjects

References

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Iranian Journal of Fuzzy Systems
Volume 23, Issue 4
July and August 2026
Pages 183-201

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