About Non-differentiable Functions

By F. Adda, Jacky Cresson. 2001

165 citations recorded by the source corpus.

Subfields: Mathematical Physics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/fcfc409857c1f1a1a4ab6a6240227693bbbfebab

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Citations in the corpus

General conformable fractional derivative and its physical interpretation (2017, background): “Actually, Kolwankar and Gangal’s LFD definition can be written as [22]”
Local fractional series expansion method for solving wave and diffusion equations on Cantor sets (2013, unknown): “In contrast, the local fractional calculus is one of the best candidates for dealing with such problems [26–44].”
Application of the Local Fractional Series Expansion Method and the Variational Iteration Method to the Helmholtz Equation Involving Local Fractional Derivative Operators (2013, background): “Local fractional calculus theory [30–44] has been used to process the nondifferentiable problems in natural phenomena.”
On chain rule for fractional derivatives (2016, background): “Authors of some papers ([11–18] and [24–28]) suggest new types of fractional derivatives and assume some usual or simplified rules for the suggested derivatives.”
On the mixed fractional Brownian motion (2006, methodology): “On the other hand, there is a clear geometrical meaning of our derivative; it gives the local Hölderian behavior of the function, and the critical order of derivation is equal to the Hölder exponent (see [1]).”
Leibniz rule and fractional derivatives of power functions (2016, unknown): “[20–40].”
Advanced Local Fractional Calculus and Its Applications (2012, unknown): “[90] F.”
Generalizations of Hölder’s and Some Related Integral Inequalities on Fractal Space (2011, background): “Fractal calculus (also called local fractional calculus) has played an important role in not only mathematics but also in physics and engineers [2-15].”
A Local Fractional Integral Inequality on Fractal Space Analogous to Anderson’s Inequality (2014, methodology): “Some of the concepts of the local fractional derivative were established in [3–26].”
Fractional embedding of differential operators and Lagrangian systems (2006, background): “Nottale [35] and results about the local fractional calculus [6].”