Powered Wendroff-type integral inequality and application to fractional PDEs

Yanlin Yang, Baishun Wang and Jun Zhou

Chaos, Solitons & Fractals, 2025, vol. 193, issue C

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.

Keywords: Wendroff inequality; Fractional partial differential equations; Singular integral inequality; Monotonization; Boundedness (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:193:y:2025:i:c:s0960077925001420

DOI: 10.1016/j.chaos.2025.116129

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