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The main aim in this paper is to use all the possible arrangements of objects such that r 1 of them are equal to 1 and r 2 (the others) of them are equal to 2, in order to generalize the definitions of Riemann-Liouville and Caputo fractional derivatives (about order 0 < β < n ) for a fuzzy-valued function. Also, we find fuzzy Laplace transforms for Riemann-Liouville and Caputo fractional derivatives about the general fractional order n - 1 < β < n under H-differentiability. Some fuzzy fractional initial value problems (FFIVPs) are solved using the above two generalizations.

Generalization of Fuzzy Laplace Transforms of Fuzzy Fractional Derivatives about the General Fractional Order n - 1 < β < n