具有非局部边界条件的非线性隐式分数阶微分方程的一些新的存在性和稳定性结果

Q1 Mathematics

Partial Differential Equations in Applied Mathematics Pub Date : 2025-03-01 DOI:10.1016/j.padiff.2025.101132

Rahman Ullah Khan , Ioan-Lucian Popa

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引用次数: 0

摘要

研究了含Hilfer-Katugampola分数阶导数的非线性隐式分数阶微分方程。利用不动点定理建立了该问题解的存在唯一性。此外，还分析了Hyers-Ulam稳定性和广义Hyers-Ulam稳定性，并通过算例验证了理论结果。

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Some novel existence and stability results for a nonlinear implicit fractional differential equation with non-local boundary conditions

This paper investigates nonlinear implicit fractional differential equations involving Hilfer-Katugampola fractional derivatives. Novel techniques are developed to establish the existence and uniqueness of solutions for the proposed problem using fixed-point theorems. Additionally, Hyers-Ulam stability and generalized Hyers-Ulam stability are analyzed, and an example is provided to validate the theoretical results.

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