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Stability analysis of the maps with variable fractional order

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  • Gade, Prashant M.
  • Bhalekar, Sachin
  • Chevala, Janardhan

Abstract

Fractional order differential and difference equations are used to model systems with memory. Variable-order fractional equations are proposed to model systems in which memory changes over time. We investigate stability conditions for linear variable order maps where the order is a periodic function with period T. We give a general procedure for arbitrary T, and for T=2 and T=3, we give exact results. For T=2, we find that the lower order determines the stability of the equations. For odd T, numerical simulations indicate that we can approximately determine the stability of the equations from the mean value of the orders.

Suggested Citation

  • Gade, Prashant M. & Bhalekar, Sachin & Chevala, Janardhan, 2026. "Stability analysis of the maps with variable fractional order," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 249(C), pages 1006-1021.
    • Handle: RePEc:eee:matcom:v:249:y:2026:i:c:p:1006-1021
    DOI: 10.1016/j.matcom.2026.06.014
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