Abstract
Fractional derivatives with fuzzy exponent defined with the help of new type of fuzzy numbers are introduced. New model of fuzzy numbers, called ordered fuzzy numbers (OFN), invented in 2003 by the author and his coworkers, is also shortly presented. The model contains all convex fuzzy numbers and allows to withdraw main drawbacks of classical operations based on the extension principle of Zadeh. It forms a tool in which calculation on fuzzy concept is rigorous and the same as with real numbers. Formulas for fractional and integral operators presented in the paper are based on Caputo definition. They generalize the concept of interval fractional derivatives. Some examples are also given.
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