Calculus, as a cornerstone of mathematics, has been an indispensable tool in the fields of science and engineering since the seventeenth century when Newton and Leibniz were active. Traditional integer-order calculus primarily deals with linear and local systems, but many systems in the real world exhibit nonlinear and global characteristics. This has prompted mathematicians to explore more generalized forms of calculus. Fractional calculus emerged in this context, allowing us to set the order of differentiation and integration operations to non-integer values, thus enabling more accurate descriptions and analysis of complex systems.

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Nabla Fractional Order Systems: Theory and Applications

  • Yiheng Wei,
  • Jinde Cao,
  • Xintong Ni,
  • Shuaiyu Zhou

摘要

Calculus, as a cornerstone of mathematics, has been an indispensable tool in the fields of science and engineering since the seventeenth century when Newton and Leibniz were active. Traditional integer-order calculus primarily deals with linear and local systems, but many systems in the real world exhibit nonlinear and global characteristics. This has prompted mathematicians to explore more generalized forms of calculus. Fractional calculus emerged in this context, allowing us to set the order of differentiation and integration operations to non-integer values, thus enabling more accurate descriptions and analysis of complex systems.