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<p>We analyze a quasilinear reaction-diffusion system containing the time-fractional Caputo derivative and prove the existence and uniqueness result for the initial-boundary problems with Dirichlet and Robin (Neumann) boundary conditions under suitable assumptions imposed on the given data. The existence of the solution to our problem is proved by using the Leray–Schauder fixed-point theorem. The positivity principle enables us to apply the method of upper-lower solutions. We provide an example of upper and lower solutions for some specific time-fractional reaction-diffusion system.</p>

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Classical Solutions of Time-Fractional Quasilinear Reaction-Diffusion Systems

  • 期刊论文

  • 发表日期：

    2025年7月1日

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  • Mykola Krasnoshchok

摘要

We analyze a quasilinear reaction-diffusion system containing the time-fractional Caputo derivative and prove the existence and uniqueness result for the initial-boundary problems with Dirichlet and Robin (Neumann) boundary conditions under suitable assumptions imposed on the given data. The existence of the solution to our problem is proved by using the Leray–Schauder fixed-point theorem. The positivity principle enables us to apply the method of upper-lower solutions. We provide an example of upper and lower solutions for some specific time-fractional reaction-diffusion system.