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<p>Starting from some general considerations about the current definitions of the fractional Laplacian operator, in this work we present an alternative definition of the fractional in space derivative. The analysis exploits the theory of the operational calculus for unbounded operators with spectrum contained in the imaginary axis. The resulting operator interpolates the derivatives of arbitrary integer order.</p>

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An alternative definition of the fractional in space derivatives

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月24日

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  • Eleonora Denich,
  • Paolo Novati

摘要

Starting from some general considerations about the current definitions of the fractional Laplacian operator, in this work we present an alternative definition of the fractional in space derivative. The analysis exploits the theory of the operational calculus for unbounded operators with spectrum contained in the imaginary axis. The resulting operator interpolates the derivatives of arbitrary integer order.