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A generalized Caputo fractional jerk equation with Caputo antiperiodic boundary conditions: Existence of solutions, stability and numerical simulations

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  • Ali, Zeeshan
  • Pinelas, Sandra

Abstract

This paper investigates the existence of solutions, stability, and numerical simulations for a generalized fractional jerk equation with fractional antiperiodic boundary conditions, both involving Caputo derivatives. The model features non-integer order derivatives in the equation and boundary conditions, resulting in a more general formulation. Fixed-point theory is employed to establish sufficient conditions for the existence and uniqueness, leading to novel results. Furthermore, Ulam-Hyers stability and its generalized form are analyzed to ensure robustness of the solutions. Examples are presented to demonstrate the applicability of the theoretical findings, with the system’s behavior and stability analyzed for various fractional orders α and β using MATLAB. A special case of the proposed system is also discussed in the conclusion.

Suggested Citation

  • Ali, Zeeshan & Pinelas, Sandra, 2026. "A generalized Caputo fractional jerk equation with Caputo antiperiodic boundary conditions: Existence of solutions, stability and numerical simulations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 245(C), pages 79-94.
    • Handle: RePEc:eee:matcom:v:245:y:2026:i:c:p:79-94
    DOI: 10.1016/j.matcom.2026.01.005
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    References listed on IDEAS

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    1. Ravi P. Agarwal & Snezhana Hristova & Donal O’Regan, 2024. "Ulam Stability for Boundary Value Problems of Differential Equations—Main Misunderstandings and How to Avoid Them," Mathematics, MDPI, vol. 12(11), pages 1-22, May.
    2. Sivashankar, M. & Sabarinathan, S. & Nisar, Kottakkaran Sooppy & Ravichandran, C. & Kumar, B.V. Senthil, 2023. "Some properties and stability of Helmholtz model involved with nonlinear fractional difference equations and its relevance with quadcopter," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    3. Edmundo Capelas de Oliveira & José António Tenreiro Machado, 2014. "A Review of Definitions for Fractional Derivatives and Integral," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-6, June.
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