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Viscoelastic Kelvin–Voigt model on Ulam–Hyer’s stability and T-controllability for a coupled integro fractional stochastic systems with integral boundary conditions via integral contractors

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  • Chalishajar, Dimplekumar
  • Kasinathan, Dhanalakshmi
  • Kasinathan, Ramkumar
  • Kasinathan, Ravikumar

Abstract

We discuss the existence, uniqueness, Ulam–Hyer’s stability, and Trajectory (T-) controllability for solutions of coupled nonlinear fractional order stochastic differential systems (FSDEs) with integral boundary conditions via integral contractors. Using Banach space, we obtain some relaxed conditions for existence and uniqueness for the mentioned problem via successive approximation techniques. Furthermore, to demonstrate the results, the concept of bounded integral contractors is combined with a fractional order coupled system using regularity conditions. The Green’s function is used to find the solution for the coupled system with boundary conditions. Through Integral Contractors (ICs), we examine the existence and uniqueness results for a higher-order nonlinear fractional coupled stochastic system with integral boundary conditions on Time Scales. Further, we develop some conditions for Ulam–Hyer’s stability for the non-linear fractional order coupled systems. To demonstrate our main result, we provide a proper example. The real-life application of a coupled fractional stochastic Kelvin–Voigt model on viscoelastic elastomer is investigated to justify the theoretical model with the numerical comparison with a single and a double fractional stochastic Kelvin–Voigt model.

Suggested Citation

  • Chalishajar, Dimplekumar & Kasinathan, Dhanalakshmi & Kasinathan, Ramkumar & Kasinathan, Ravikumar, 2025. "Viscoelastic Kelvin–Voigt model on Ulam–Hyer’s stability and T-controllability for a coupled integro fractional stochastic systems with integral boundary conditions via integral contractors," Chaos, Solitons & Fractals, Elsevier, vol. 191(C).
    • Handle: RePEc:eee:chsofr:v:191:y:2025:i:c:s0960077924013377
    DOI: 10.1016/j.chaos.2024.115785
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    References listed on IDEAS

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    1. Wang, Xue & Luo, Danfeng & Zhu, Quanxin, 2022. "Ulam-Hyers stability of caputo type fuzzy fractional differential equations with time-delays," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    2. Chalishajar, Dimplekumar & Kasinathan, Dhanalakshmi & Kasinathan, Ramkumar & Kasinathan, Ravikumar, 2024. "Exponential stability, T-controllability and optimal controllability of higher-order fractional neutral stochastic differential equation via integral contractor," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    3. Rhaima, Mohamed, 2023. "Ulam–Hyers stability for an impulsive Caputo–Hadamard fractional neutral stochastic differential equations with infinite delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 210(C), pages 281-295.
    4. Dimplekumar Chalishajar & Avadhesh Kumar, 2018. "Existence, Uniqueness and Ulam’s Stability of Solutions for a Coupled System of Fractional Differential Equations with Integral Boundary Conditions," Mathematics, MDPI, vol. 6(6), pages 1-12, June.
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