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Fuzzy solutions of nonlinear fractional differential equations via fuzzy fractional G -transform
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DOI：10.1016/j.fss.2026.110015.png)
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Abstract
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In this paper, we investigate the fuzzy novel hybrid approach establish using the fuzzy fractional generalized integral transform method (fuzzy fractional G-transform) and fuzzy fractional derivatives. The fuzzy homotopy analysis method is combined with fuzzy fractional G-transform to solve fuzzy nonlinear fractional differential equations (FNFDEs). Additionally, we introduce a hybrid approach termed the fuzzy fractional generalized homotopy analysis method (GHAM) to solve the European options pricing problem (EOPP) using the fuzzy Black–Scholes model. Using the h-curve, the convergence region of the fuzzy Black–Scholes model solutions is readily recognized, and fuzzy fractional GHAM is used to obtain the closed-form series solutions. To validate the convergence of the suggested series solutions, a sequence of errors is generated by estimating the difference between the exact solution and the series solution, with several terms in the series increased. Furthermore, we introduce the concept of the fuzzy modified Riemann–Liouville derivative with the Mittag–Leffler function as a kernel for the fuzzy fractional G-transform (FFG-T). The fuzzy homotopy analysis is used to develop a fuzzy hybrid fractional GHAM based on the fuzzy modified Riemann-Liouville derivative, abbreviated as MRGHAM. We discuss the advantages of the fuzzy fractional MRGHAM and use it to solve FNFDEs. Finally, we apply the fuzzy fractional MRGHAM, fuzzy Adomian decomposition method, fuzzy homotopy perturbation method, and fuzzy variational iteration method to formulate a fuzzy fractional non-fatal disease epidemic model. The fuzzy fractional power epidemic model is simplified to a simple epidemic model, and the results demonstrate great agreement with the standard approaches. We supply plots to show the simplicity and reliability of the techniques.
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