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The first part of the chapter concerns the construction of nonlocal dynamical systems associated with scalar Caputo fractional differential equations and triangular systems. The key point is to establish the existence of a nonlocal two-parameter flow generated by their solutions. The second part deals with operator semi-groups associated with integral equations with degenerate kernels associated with initial value problems of Caputo fractional differential equations in finite-dimensional spaces.

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Caputo Dynamical Systems

  • 章节

  • 发表日期：

    2025年

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  • Thai Son Doan,
  • Peter E. Kloeden,
  • Hoang The Tuan

摘要

The first part of the chapter concerns the construction of nonlocal dynamical systems associated with scalar Caputo fractional differential equations and triangular systems. The key point is to establish the existence of a nonlocal two-parameter flow generated by their solutions. The second part deals with operator semi-groups associated with integral equations with degenerate kernels associated with initial value problems of Caputo fractional differential equations in finite-dimensional spaces.