On calculus of local fractional derivatives

By Azizollah Babakhani, Varsha Daftardar-Gejji. 2002

164 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/e48e08c4be4d34e8f2587c01117c0036625b93c4

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In Applied Mathematics

In Mathematical Physics

In Modeling and Simulation

Citations in the corpus

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].”
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].”
Advanced Local Fractional Calculus and Its Applications (2012, unknown): “[44] A.”
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.”
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.”
Calculus on fractal subsets of real line - I: formulation (2003, methodology): “As examples, we discuss a fractal-time diffusion equation, and one dimensional motion of a particle undergoing friction in a fractal medium.”
On novel nondifferentiable exact solutions to local fractional Gardner's equation using an effective technique (2020, background): “FIGURE 1 Profile of solution displayed in (23) for ν = ln(2)∕ ln(3), and ρ2 = 0.”
A remark on local fractional calculus and ordinary derivatives (2016, background): “As it was mentioned in [6], “These definitions, however, are non-local in nature, which makes them unsuitable for investigating properties related to local scaling or fractional differentiability".”
Generalized Convex Functions on Fractal Sets and Two Related Inequalities (2014, unknown): “Many researchers studied the properties of functions on fractal space and constructedmany kinds of fractional calculus by using different approaches (see [10–14]).”