带时间尺度纳布拉导数的分数阶序列线性微分方程

Axioms Pub Date : 2024-07-01 DOI:10.3390/axioms13070447
Cheng-Cheng Zhu, Jiang Zhu
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引用次数: 0

摘要

本文提出了具有黎曼-刘维尔纳布拉导数和卡普托纳布拉导数的分数阶序列微分方程在时间尺度上的一般理论。利用∇-Mittag-Leffler 函数、拉普拉斯变换法、运算法和运算分解法,给出了常数系数情况下同质和非同质问题的显式解。此外,我们还提供了使用拉普拉斯变换方法求解一类新的具有卷积型可变系数的分数阶序列微分方程的一些结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Fractional-Order Sequential Linear Differential Equations with Nabla Derivatives on Time Scales
In this paper, we present a general theory for fractional-order sequential differential equations with Riemann–Liouville nabla derivatives and Caputo nabla derivatives on time scales. The explicit solution, in the case of constant coefficients, for both the homogeneous and the non-homogeneous problems, are given using the ∇-Mittag-Leffler function, Laplace transform method, operational method and operational decomposition method. In addition, we also provide some results about a solution to a new class of fractional-order sequential differential equations with convolutional-type variable coefficients using the Laplace transform method.
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