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Explicit solutions of fractional differential equations with uncertainty. (English) Zbl 1259.34009

Summary: 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.

MSC:

34A08 Fractional ordinary differential equations
34A07 Fuzzy ordinary differential equations
34A05 Explicit solutions, first integrals of ordinary differential equations
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