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<p>We construct an inverse operator for integro-differential operators of distributed order. The inverse operator is represented as a convolution operator with a kernel expressed in terms of the distributed parameter Wright function. Inversion formulas, as well as Newton–Leibniz formulas, are proved for operators of distributed order differentiation and integration, understood both in the Riemann–Liouville sense and in the Gerasimov–Caputo sense.</p>

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Inversion formulas for distributed order integration and differentiation operators

  • 期刊论文

  • 发表日期：

    2025年1月3日

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  • Arsen V. Pskhu

摘要

We construct an inverse operator for integro-differential operators of distributed order. The inverse operator is represented as a convolution operator with a kernel expressed in terms of the distributed parameter Wright function. Inversion formulas, as well as Newton–Leibniz formulas, are proved for operators of distributed order differentiation and integration, understood both in the Riemann–Liouville sense and in the Gerasimov–Caputo sense.