On the local fractional derivative of everywhere non-differentiable continuous functions on intervals

DOI10.1016/j.cnsns.2016.05.029zbMath1473.26007OpenAlexW2417049975MaRDI QIDQ2004803

Cheng-Shi Liu

Publication date: 7 October 2020

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2016.05.029

zbMATH Keywords

fractional calculuslocal fractional derivativenon-differentiable function

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives (26A27)

Related Items (7)

A modified quasi-boundary value method for a backward problem for the inhomogeneous time conformable fractional heat equation in a cylinder ⋮ Counterexamples on Jumarie's three basic fractional calculus formulae for non-differentiable continuous functions ⋮ Comments on various extensions of the Riemann-Liouville fractional derivatives: about the Leibniz and chain rule properties ⋮ No nonlocality. No fractional derivative ⋮ Exactly solving some typical Riemann–Liouville fractional models by a general method of separation of variables ⋮ Lie symmetry and exact solution of the time-fractional Hirota-Satsuma Korteweg-de Vries system ⋮ A new computational approach for solving nonlinear local fractional PDEs

Cites Work

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• What is a fractional derivative?
• No violation of the Leibniz rule. No fractional derivative
• Counterexamples on Jumarie's two basic fractional calculus formulae
• Table of some basic fractional calculus formulae derived from a modified Riemann-Liouville derivative for non-differentiable functions
• On the local fractional derivative
• A new definition of fractional derivative
• Corrigendum to ``About non-differentiable functions
• Local fractional derivatives of differentiable functions are integer-order derivatives or zero
• Fractional differentiability of nowhere differentiable functions and dimensions
• About non-differentiable functions

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