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Fuzzy discrete fractional granular calculus and its application to fractional cobweb models

Author

Listed:
  • Liu, Xuelong
  • Ye, Guoju
  • Liu, Wei
  • Shi, Fangfang

Abstract

This work aims to solve a fuzzy initial value problem for fractional difference equations and to study a class of discrete fractional cobweb models with fuzzy data under the Caputo granular difference operator. Based on relative-distance-measure fuzzy interval arithmetic, we first present several new concepts for fuzzy functions in the field of fuzzy discrete fractional calculus, such as the forward granular difference operator, Riemann-Liouville fractional granular sum, Riemann-Liouville and Caputo granular differences. The composition rules and Leibniz laws used to solve a fuzzy initial value problem for fractional difference equations are also presented. As applications, we obtain the solutions of fuzzy discrete Caputo fractional cobweb models, provide conditions for the convergence of the solution to the equilibrium value, and discuss different cases of how the trajectory of the granular solution converges to the equilibrium value. The developed results are also illustrated through several numerical examples.

Suggested Citation

  • Liu, Xuelong & Ye, Guoju & Liu, Wei & Shi, Fangfang, 2025. "Fuzzy discrete fractional granular calculus and its application to fractional cobweb models," Applied Mathematics and Computation, Elsevier, vol. 489(C).
    • Handle: RePEc:eee:apmaco:v:489:y:2025:i:c:s0096300324006374
    DOI: 10.1016/j.amc.2024.129176
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    References listed on IDEAS

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    1. Li, Xin & Ma, Weiyuan & Bao, Xionggai, 2024. "Generalized fractional calculus on time scales based on the generalized Laplace transform," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    2. Shi, Fangfang & Ye, Guoju & Liu, Wei & Zhao, Dafang, 2023. "A class of nonconvex fuzzy optimization problems under granular differentiability concept," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 211(C), pages 430-444.
    3. Bohner, Martin & Jonnalagadda, Jagan Mohan, 2022. "Discrete fractional cobweb models," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    4. Wu, Guo-Cheng & Baleanu, Dumitru & Luo, Wei-Hua, 2017. "Lyapunov functions for Riemann–Liouville-like fractional difference equations," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 228-236.
    5. Guo, Yating & Ye, Guoju & Liu, Wei & Zhao, Dafang & Treanţă, Savin, 2022. "On symmetric gH-derivative: Applications to dual interval-valued optimization problems," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
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