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.
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The authors wish to thank the editor in chief, the editor and the anonymous reviewers for their constructive comments on this study.
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Allahviranloo, T., Salahshour, S. & Abbasbandy, S. Explicit solutions of fractional differential equations with uncertainty. Soft Comput 16, 297–302 (2012). https://doi.org/10.1007/s00500-011-0743-y
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DOI: https://doi.org/10.1007/s00500-011-0743-y