Explicit solutions of fractional differential equations with uncertainty

Abstract

We give the explicit solutions of uncertain fractional differential equations (UFDEs) under Riemann–Liouville H-differentiability using Mittag-Leffler functions. To this end, Riemann–Liouville H-differentiability is introduced which is a direct generalization of the concept of Riemann–Liouville differentiability in deterministic sense to the fuzzy context. Moreover, equivalent integral forms of UFDEs are determined which are applied to derive the explicit solutions. Finally, some illustrative examples are given.