Differential Equations and Dynamical Systems

, Volume 26, Issue 1–3, pp 265–277 | Cite as

A Novel Fractional Microbial Batch Culture Process and Parameter Identification

  • Pan Mu
  • Lei WangEmail author
  • Yi An
  • Yanping Ma
Original Research


This paper considers the microbial batch culture for producing 1,3-propanediol(1,3-PD) via glycerol disproportionation. Due to the nature of the fractional order operations, a novel fractional order model, which is based upon the original ordinary differential dynamic system, is introduced to describe the complex bioprocess in a more accurate manner. Existence and uniqueness of solutions to the novel fractional order system and the continuity of solutions with respect to the parameters are discussed respectively. In addition, a parameter identification problem of the system is presented, and a particle swarm optimization algorithm is constructed to solve it. Finally, the conclusion is drawn by numerical simulations.


Fractional order model Microbial batch culture Parameter identification PSO algorithm 

Mathematics Subject Classification

34A08 34K37 35Q92 92B05 



This work was supported by the National Natural Science Foundation for the Youth of China (Grant No. 11401073), and the Fundamental Research Funds for Central Universities in China (Grant DUT15LK25).


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Copyright information

© Foundation for Scientific Research and Technological Innovation 2017

Authors and Affiliations

  1. 1.School of Mathematical SciencesDalian University of TechnologyDalianPeople’s Republic of China
  2. 2.School of Control Science and EngineeringDalian University of TechnologyDalianPeople’s Republic of China
  3. 3.Department of MathematicsLoyola Marymount UniversityLos AngelesUSA

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