Studies of fractal structures and processes using methods of fractional calculus

TL;DR

This paper explores the application of fractional calculus to fractal structures, introducing local fractional derivatives and their use in modeling fractal functions and equations like the local fractional Fokker-Planck equation.

Contribution

It introduces the concept of local fractional derivatives and applies them to fractal functions and equations, advancing the mathematical tools for fractal analysis.

Findings

Development of local fractional derivative concept

Application to fractal and multifractal functions

Formulation of local fractional Fokker-Planck equation

Abstract

The thesis deals with applications of fractional calculus to fractals. It introduces the notion of local fractional derivative (LFD). Fractal and multifractal functions have been studied in the thesis using LFD. New kind of equations are introduced which involve LFD and one example, local fractional Fokker-Planck equation, is studied in detail.