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Mathematical analysis of the Cauchy type dynamical system under piecewise equations with Caputo fractional derivative

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  • Shah, Kamal
  • Abdeljawad, Thabet
  • Ali, Arshad

Abstract

This research work is related to study the Cauchy type dynamical system under piecewise equations with fractional order Caputo derivative. Using traditional fixed point tools due to Banach and Schauder, the required results for the existence and uniqueness are developed. Since stability analysis is an important aspect of the aforesaid analysis, so we also attempt on Hyers-Ulam (HU) type stability results for the proposed system. For this purposes, we use tools of nonlinear functional analysis. Further a numerical method based on Newton polynomials of interpolation is applied to compute approximate solution for the considered system. For application and validity purpose of our main results, we give two illustrative examples.

Suggested Citation

  • Shah, Kamal & Abdeljawad, Thabet & Ali, Arshad, 2022. "Mathematical analysis of the Cauchy type dynamical system under piecewise equations with Caputo fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    • Handle: RePEc:eee:chsofr:v:161:y:2022:i:c:s0960077922005665
    DOI: 10.1016/j.chaos.2022.112356
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    References listed on IDEAS

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    1. Atangana, Abdon & İğret Araz, Seda, 2021. "New concept in calculus: Piecewise differential and integral operators," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    2. Zhang, Tianwei & Li, Yongkun, 2022. "S-asymptotically periodic fractional functional differential equations with off-diagonal matrix Mittag-Leffler function kernels," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 331-347.
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    1. Selvam, Anjapuli Panneer & Govindaraj, Venkatesan, 2024. "Investigation of controllability and stability of fractional dynamical systems with delay in control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 89-104.

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