Fuzzification of Fractal Calculus
Alireza Khalili Golmankhaneh, Kerri Welch, Cristina Serpa, Palle E. T., J{\o}rgensen
TL;DR
This paper introduces a novel framework called fractal fuzzy calculus, combining fractal and fuzzy calculus concepts to define derivatives and integrals for fuzzy functions with fractal support, and solves related differential equations.
Contribution
It formulates the first comprehensive framework of fractal fuzzy calculus, including derivatives, integrals, and differential equations involving fuzzy functions with fractal support.
Findings
Defined fractal fuzzy derivatives and integrals
Formulated and solved various fractal fuzzy differential equations
Established a new mathematical framework for fuzzy calculus on fractals
Abstract
In this manuscript, fractal and fuzzy calculus are summarized. Fuzzy calculus in terms of fractal limit, continuity, its derivative, and integral are formulated. The fractal fuzzy calculus is a new framework that includes fractal fuzzy derivatives and fractal fuzzy integral. In this framework, fuzzy number-valued functions with fractal support are the solutions of fractal fuzzy differential equations. Different kinds of fractal fuzzy differential equations are given and solved.
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Taxonomy
TopicsFuzzy Systems and Optimization