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<p>In this paper, we mainly consider the monotonicity of solutions for nonlocal uniformly fractional parabolic equations in the whole space. We first adopt a generalized weighted average inequality which is similar to Theorem <InternalRef RefID="FPar3">1.3</InternalRef> in [<CitationRef CitationID="CR12">12</CitationRef>]. Then, applying the sliding method, we derive the monotonicity of solutions for the uniformly fractional parabolic equations. The core idea of this method involves comparing the solution’s values at two distinct points. One point is derived by sliding the domain in a given direction, then the domain is slided back to a limiting position for analysis.</p>

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Monotonicity of solutions for nonlocal uniformly fractional parabolic equations in the whole space

  • 期刊论文

  • 发表日期：

    2026年3月9日

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  • Yanjuan Tang

摘要

In this paper, we mainly consider the monotonicity of solutions for nonlocal uniformly fractional parabolic equations in the whole space. We first adopt a generalized weighted average inequality which is similar to Theorem 1.3 in [12]. Then, applying the sliding method, we derive the monotonicity of solutions for the uniformly fractional parabolic equations. The core idea of this method involves comparing the solution’s values at two distinct points. One point is derived by sliding the domain in a given direction, then the domain is slided back to a limiting position for analysis.