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<p>This paper presents results on general fractional operators with Sonine kernels for fuzzy functions. We begin by introducing new general fractional integrals and derivatives using generalized Hukuhara differentiability (gH-differentiability), and then analyze some of their properties. Building upon this, an initial value problem of fuzzy fractional differential equations under the Caputo type general fractional derivative is investigated using fuzzy Laplace transform techniques. The obtained analytical solutions are expressed through convolution series, effectively expanding the traditional power series of exponential and Mittag–Leffler functions. Finally, we provide several numerical examples to illustrate and validate the developed results.</p>

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Fuzzy general fractional operators with Sonine kernels under gH-differentiability

  • 期刊论文

  • 发表日期：

    2025年8月8日

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  • Xuelong Liu,
  • Guoju Ye,
  • Wei Liu

摘要

This paper presents results on general fractional operators with Sonine kernels for fuzzy functions. We begin by introducing new general fractional integrals and derivatives using generalized Hukuhara differentiability (gH-differentiability), and then analyze some of their properties. Building upon this, an initial value problem of fuzzy fractional differential equations under the Caputo type general fractional derivative is investigated using fuzzy Laplace transform techniques. The obtained analytical solutions are expressed through convolution series, effectively expanding the traditional power series of exponential and Mittag–Leffler functions. Finally, we provide several numerical examples to illustrate and validate the developed results.