Exact Solutions for Classes of Nonlinear Differential Equations on Fractal Supports

TL;DR

This paper derives exact solutions for specific nonlinear differential equations on fractal supports, highlighting the Riccati-type equation and its link to the Schrödinger equation, advancing understanding of differential equations on fractals.

Contribution

It introduces explicit solutions for nonlinear fractal differential equations and explores their connection to quantum mechanics through the Schrödinger equation.

Findings

Exact solutions for Riccati-type fractal differential equations

Connection established between fractal Riccati equations and Schrödinger equation

Enhanced understanding of differential equations on fractal supports

Abstract

In this paper, the exact solutions of certain non-linear differential equations defined on a fractal subset of the real line are presented. Particular attention is paid to the Riccati-type fractal differential equation, for which a connection with the Schrodinger equation is also provided.