关于共形导数的性质及其在物理中的应用
On the nature of the conformable derivative and its applications to physics
摘要：
这项工作的目的是表明，哈利勒和Katagampoula一致的衍生物是等价的变量$x$ $\rightarrow $ $x^{α}/α,$的简单变化，其中$α$是阶的衍生操作，当应用到微分函数。虽然这意味着没有\textquotedblleft新的数学\textquotedblright \是通过这些衍生物的工作，这是这项工作的第二个目的，认为仍然有重要的价值，在探索这些衍生物的数学和物理应用。这项工作认为，线性微分方程，自伴性，斯特姆刘维系统，积分变换。这项工作的第三个目的是有助于物理解释时，这些衍生物被应用于物理和工程。量子力学是这一发展的主要背景。
英文摘要：
The purpose of this work is to show that the Khalil and Katagampoula conformable derivatives are equivalent to the simple change of variables $x$ $\rightarrow $ $x^{α}/α,$ where $α$ is the order of the derivative operator, when applied to differential functions. Although this means no \textquotedblleft new mathematics\textquotedblright\ is obtained by working with these derivatives, it is a second purpose of this work to argue that there is still significant value in exploring the mathematics and physical applications of these derivatives. This work considers linear differential equations, self-adjointness, Sturm-Liouville systems, and integral transforms. A third purpose of this work is to contribute to the physical interpretation when these derivatives are applied to physics and engineering. Quantum mechanics serves as the primary backdrop for this development.
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