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In this paper, we construct a system for analysis of an analytic solution of fractional fuzzy solitary wave solutions for the Korteweg–De Vries (KdV) equation. We apply the iterative method and the Laplace transform under the fractional Caputo-Fabrizio operator. The obtained series form the solution was calculated and approached the estimate values of the proposed problems. The upper and lower portions of the fuzzy result in all three problems were simulation applying two different fractional order among zero and one. The fractional operator is nonsingular and global since the exponential function is present. It provides all types of fuzzy results occurring among zero and one at any fractional order because its dynamic behaviour is globalised of the suggested problems. Because the fuzzy number provides the result in a fuzzy form, with lower and upper branches, fuzziness is also incorporated in the unknown quantity.

Analysis of the Fuzzy Fractional-Order Solitary Wave Solutions for the KdV Equation in the Sense of Caputo-Fabrizio Derivative