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Convergence and Stability of Series Solutions for Fuzzy Fractional Integrals |
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PP: 651-663 |
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doi:10.18576/amis/200306
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Author(s) |
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Suleiman Shelash Al-Hawary,
Nandhini Devi S.,
Yogeesh N.,
Asokan Vasudevan,
N. Raja,
Mohammad Hunitie,
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Abstract |
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| Fuzzy fractional integrals extend classical fractional calculus to contexts with uncertainty, enabling modeling of memory-dependent processes with imprecise data. In this study, we develop a systematic level-cut formulation of the fuzzy Riemann Liouville integral operator on 𝐶([𝑎,𝑏];F(R)), derive a power-series ansatz for linear fuzzy fractional integral equations, and establish recursive relations for fuzzy coefficients. Convergence is rigorously analyzed via fuzzy-norm adaptations of the ratio and root tests, yielding a geometric growth condition under which uniform convergence holds. Ulam-Hyers and Ulam-Hyers-Rassias stability are proved by constructing contraction estimates in the fuzzy-norm. Illustrative examples and counterexamples confirm the sharpness of the theoretical criteria, and numerical bounds quantify geometric error decay. Extensions to generalized fractional operators and nonlinear fuzzy integral equations demonstrate the frameworks flexibility. These results show that fuzziness preserves the classical convergence domain while introducing interval-width considerations, furnishing a solid foundation for further theoretical developments and numerical algorithms in fuzzy fractional calculus. |
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