Using Fractional Derivatives to Generalize the Hodgkin–Huxley Model

  • Hany H. Sherief
  • A. M. A. El-Sayed
  • S. H. Behiry
  • W. E. Raslan


In this work the methodology of fractional calculus is used to formulate a new generalized fractional of the Hodgkin and Huxley model for action-potential of a neuron. The Caputo fractional derivative is used in this model. A numerical algorithm based on the predictor corrector method is used to obtain the solution of the model. The results showed that as the fractional derivative order tends to unity the original model is retained. Every change in the fractional order gave a new response for membrane voltage. We believe that by changing this order, the action potential of some organism may be modeled well.


Fractional Order Fractional Derivative Fractional Calculus Fractional Differential Equation Potassium Conductance 
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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Hany H. Sherief
    • 1
  • A. M. A. El-Sayed
    • 1
  • S. H. Behiry
    • 2
  • W. E. Raslan
    • 3
  1. 1.Department of Mathematics, Faculty of ScienceUniversity of AlexandriaAlexandriaEgypt
  2. 2.General Required Courses DepartmentJeddah Community College, King Abdulaziz UniversityJeddahKingdom of Saudi Arabia
  3. 3.Mathematics and Engineering Physics Department, Faculty of EngineeringUniversity of MansouraMansouraEgypt

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