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This research explores the application of operator theory within the context of grand Lebesgue spaces, considering the field of linear systemsLinear system. The study is focused on analytical approaches to reconstructing an input signal in a linear systemLinear system described by a negative-fractional order transfer functionFractional order transfer function. ConvolutionConvolution with the corresponding impulse response function is interpreted as the Riemann–Liouville fractional integral, and therefore, the problem is considered within the application ofFractional calculus fractional calculus on the generalized grand Lebesgue spacesGeneralized grand Lebesgue space. The fractional order integral equation, which formalizes the zero-state response of the system, is solved in terms of the Neumann seriesNeumann series and the range of its validity is described.

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Analytical Input Signal Restoration in a Grand Lebesgue Space for Linear Systems with Negative-Fractional Order Transfer Functions

  • 会议论文

  • 发表日期：

    2025年

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  • Yuri Drobotov

摘要

This research explores the application of operator theory within the context of grand Lebesgue spaces, considering the field of linear systemsLinear system. The study is focused on analytical approaches to reconstructing an input signal in a linear systemLinear system described by a negative-fractional order transfer functionFractional order transfer function. ConvolutionConvolution with the corresponding impulse response function is interpreted as the Riemann–Liouville fractional integral, and therefore, the problem is considered within the application ofFractional calculus fractional calculus on the generalized grand Lebesgue spacesGeneralized grand Lebesgue space. The fractional order integral equation, which formalizes the zero-state response of the system, is solved in terms of the Neumann seriesNeumann series and the range of its validity is described.