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Fractional-Order Systems

Author

Listed:
  • Chongyang Liu

    (Shandong Technology and Business University, School of Mathematics and Information Science)

  • Song Wang

    (Curtin University, School of Electrical Engineering, Computing, and Mathematical Sciences)

  • Zhaohua Gong

    (Shandong Technology and Business University, School of Mathematics and Information Science)

Abstract

In this chapter, we review some basic concepts and theorems of fractional-order systems including ordinary differential equations with the Riemann-Liouville, Caputo, Atangana-Baleanu and conformable fractional derivatives, and delay differential equations with Caputo fractional derivatives. Furthermore, we develop two classes of numerical methods for solving fractional ordinary differential equations. The convergence rates of these numerical schemes are also analyzed. Finally, numerical examples are solved to verify the theoretical results of the proposed numerical methods.

Suggested Citation

  • Chongyang Liu & Song Wang & Zhaohua Gong, 2026. "Fractional-Order Systems," Springer Optimization and Its Applications,, Springer.
    • Handle: RePEc:spr:spochp:978-981-92-0274-4_3
    DOI: 10.1007/978-981-92-0274-4_3
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