Here the theory of local fractional differential equations is extended to a more general class of equations akin to usual exact differential equations. In the process, a new notion has been introduced which is termed as $\alpha$-exact local fractional differential equation. The theory of such equations parallels that for the first order ordinary differential equations. A criterion to check the $\alpha$-exactness emerges naturally and also a method to find general solutions of such equations. This development completes the basic theory of the local fractional differential equations. The solved examples demonstrate how complex functions arise as solutions which will be useful in understanding the processes taking place on fractals.

在这里，局部分数阶微分方程的理论被扩展到更一般的方程类，类似于通常的精确微分方程。在这个过程中，引入了一个新的概念，称为$\alpha$- 精确的局部分数阶微分方程。这种方程的理论与一阶常微分方程的理论相似。检查的标准$\alpha$- 精确性自然出现，也是寻找此类方程的一般解的方法。这一发展完善了局部分数阶微分方程的基本理论。求解的例子展示了复杂函数如何作为解决方案出现，这将有助于理解分形上发生的过程。