Separable local fractional differential equations

TL;DR

This paper explores the extension and solution methods of separable local fractional differential equations, highlighting their ability to incorporate fractal sets and analyze local scaling behavior of functions.

Contribution

It introduces new approaches for solving separable local fractional differential equations and extends their scope to include various functions.

Findings

Extended the scope of local fractional differential equations

Developed methods for solving separable local fractional equations

Demonstrated incorporation of fractal sets into equations

Abstract

The concept of local fractional derivative was introduced in order to be able to study the local scaling behavior of functions. However it has turned out to be much more useful. It was found that simple equations involving these operators naturally incorporate the fractal sets into the equations. Here, the scope of these equations has been extended further by considering different possibilities for the known function. We have also studied a separable local fractional differential equation along with its method of solution.