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The main aim in this paper is to use all the possible arrangements of objects such that r1 of them are equal to 1 and r2 (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

mathematical problems in engineering

Generalization of Fuzzy Laplace Transforms of Fuzzy Fractional Derivatives about the General Fractional Order<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>n</mml:mi><mml:mo>-</mml:mo><mml:mn>1</mml:mn><mml:mo>&lt;</mml:mo><mml:mi>β</mml:mi><mml:mo>&lt;</mml:mo><mml:mi>n</mml:mi></mml:math>

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