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Powered Wendroff-type integral inequality and application to fractional PDEs

Author

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  • Yang, Yanlin
  • Wang, Baishun
  • Zhou, Jun

Abstract

In this paper, we generalize a powered Gronwall inequality with two variables, i.e. so-called powered Wendroff inequality. We get the recursive estimate and boundedness of its solutions. Further, we exhibit that our inequality can be used to study the boundary value problems of Caputo fractional PDEs, such as uniqueness, boundedness and continuous dependence of solutions. Finally, we give two concrete examples.

Suggested Citation

  • Yang, Yanlin & Wang, Baishun & Zhou, Jun, 2025. "Powered Wendroff-type integral inequality and application to fractional PDEs," Chaos, Solitons & Fractals, Elsevier, vol. 193(C).
    • Handle: RePEc:eee:chsofr:v:193:y:2025:i:c:s0960077925001420
    DOI: 10.1016/j.chaos.2025.116129
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    References listed on IDEAS

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    1. Wang, Fei & Zhang, Chuan & Yang, Yongqing & Li, Ning, 2023. "Observer-based consensus of fractional order parabolic PDEs agents on directed networks via boundary communication," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
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