A NEW FRACTAL DERIVATION

By Ji-Huan He. 2011

173 citations recorded by the source corpus.

A new fractal derive is defined, which is very easy for engineering applications to discontinuous problems, two simple examples are given to elucidate to establish governing equations with fractal derive and how to solve such equations, respectively.

Subfields: Modeling and Simulation, Numerical Analysis, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/74e51e475d524298df21cce2a5f4b9f6c1ddd4c7

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Modeling and Simulation

In Numerical Analysis

In Statistical and Nonlinear Physics

Citations in the corpus

A Tutorial Review on Fractal Spacetime and Fractional Calculus (2014, unknown): “Definition 9 Hereby we introduce another fractal derivative in the form [65]”
Fractal heat conduction problem solved by local fractional variation iteration method (2013, methodology): “In case of fractal objects the fractal Fourier law should be used [5-7] in contrast to the continuous case when both the classical and the fractional versions are valid [8-18].”
New promises and future challenges of fractal calculus: From two-scale thermodynamics to fractal variational principle (2020, background): “Before proceeding further, we first give some definitions and theorems on fractal calculus for easy understanding [7, 61-64].”
Fractional derivatives of constant and variable orders applied to anomalous relaxation models in heat-transfer problems (2016, methodology): “Fractional derivatives (FDs) were utilized to model the complex phenomenon in science and engineering practice [1,2,3,4,5,6,7].”
Advanced Local Fractional Calculus and Its Applications (2012, unknown): “[135] J.”
New Fractional Derivatives with Nonlocal and Non-Singular Kernel: Theory and Application to Heat Transfer Model (2016, background): “We recall here that another derivative was introduced in [17, 18] with the aim of solving some problems within the scope of thermal science.”