Exact local fractional differential equations

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. (C) 2021 Published by Elsevier Ltd.