一类阶数从一到二的ψ-Caputo时间分数阶系统的温和解的存在性与唯一性
Existence and uniqueness of mild solutions for a class of psi-Caputo time-fractional systems of order from one to two
AI总结：
本文针对Banach空间中导数阶数1到2的ψ-Caputo时间分数阶演化系统，利用余弦/正弦族算子与广义拉普拉斯变换导出温和解的积分表达式，并通过不动点技术与Grönwall不等式证明其存在唯一性。
摘要：
我们证明了在Banach空间中，一类导数阶数从1到2的特定时间分数阶ψ-Caputo演化系统的温和解的存在性与唯一性。通过利用余弦和正弦族算子的性质，以及广义拉普拉斯变换，我们推导出了温和解的一个更简洁的表达式。该表达式以积分形式表述，并包含了Mainardi的Wright型函数。此外，我们提供了与温和解中出现的算子相关的各种有价值的性质。另外，运用不动点技术和Grönwall不等式，我们确立了温和解的存在性与唯一性。为了说明我们的结果，我们以一个时间分数阶方程为例，给出了其对应温和解的表达式。
英文摘要：
We prove the existence and uniqueness of mild solutions for a specific class of time-fractional $ψ$-Caputo evolution systems with a derivative order ranging from 1 to 2 in Banach spaces. By using the properties of cosine and sine family operators, along with the generalized Laplace transform, we derive a more concise expression for the mild solution. This expression is formulated as an integral, incorporating Mainardi's Wright-type function. Furthermore, we provide various valuable properties associated with the operators present in the mild solution. Additionally, employing the fixed-point technique and Grönwall's inequality, we establish the existence and uniqueness of the mild solution. To illustrate our results, we conclude with an example of a time-fractional equation, presenting the expression for its corresponding mild solution.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
