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Sufficient Conditions for the Non-Existence of Global Solutions to Fractional Systems with Lower-Order Hadamard-Type Fractional Derivatives

Author

Listed:
  • Saeed M. Ali

    (Department of Basic Engineering Sciences, College of Engineering, Imam Abdulrahman Bin Faisal University, P.O. Box 1982, Dammam 34151, Saudi Arabia)

  • Mohammed D. Kassim

    (Department of Basic Engineering Sciences, College of Engineering, Imam Abdulrahman Bin Faisal University, P.O. Box 1982, Dammam 34151, Saudi Arabia)

Abstract

This study investigates the absence of global solutions for a system of fractional differential equations. The system features a nonlinear source term with nonlocal temporal behavior and involves two Hadamard fractional derivatives (HFDs) of varying orders. Compared to previous studies, this system offers greater generality. To establish our conclusions, we employ properties of fractional derivatives, the method of test function, and integral inequality techniques. Finally, illustrative examples showcase our findings.

Suggested Citation

  • Saeed M. Ali & Mohammed D. Kassim, 2025. "Sufficient Conditions for the Non-Existence of Global Solutions to Fractional Systems with Lower-Order Hadamard-Type Fractional Derivatives," Mathematics, MDPI, vol. 13(7), pages 1-16, March.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:7:p:1031-:d:1617763
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    References listed on IDEAS

    as
    1. Tatar, Nasser-eddine, 2008. "Nonexistence results for a fractional problem arising in thermal diffusion in fractal media," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1205-1214.
    2. Aljoudi, Shorog & Ahmad, Bashir & Nieto, Juan J. & Alsaedi, Ahmed, 2016. "A coupled system of Hadamard type sequential fractional differential equations with coupled strip conditions," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 39-46.
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