Results 1 to 10 of about 317,193 (185)

Fractal Calculus on Fractal Interpolation Functions [PDF]

Fractal and Fractional, 2021
In this paper, fractal calculus, which is called Fα-calculus, is reviewed. Fractal calculus is implemented on fractal interpolation functions and Weierstrass functions, which may be non-differentiable and non-integrable in the sense of ordinary calculus.
Arulprakash Gowrisankar, Alireza Khalili Golmankhaneh, Cristina Serpa   +2 more
doaj   +4 more sources

The Fractal Calculus for Fractal Materials [PDF]

Fractal and Fractional, 2019
The major problem in the process of mixing fluids (for instance liquid-liquid mixers) is turbulence, which is the outcome of the function of the equipment (engine). Fractal mixing is an alternative method that has symmetry and is predictable.
Fakhri Khajvand Jafari, Mohammad Sadegh Asgari, Amir Pishkoo   +2 more
doaj   +3 more sources

Fractal calculus and its geometrical explanation

Results in Physics, 2018
Fractal calculus is very simple but extremely effective to deal with phenomena in hierarchical or porous media. Its operation is almost same with that by the advanced calculus, making it much accessible to all non-mathematicians.
Ji-Huan He
doaj   +3 more sources

Fractal Derivatives, Fractional Derivatives and q-Deformed Calculus [PDF]

Entropy, 2023
This work presents an analysis of fractional derivatives and fractal derivatives, discussing their differences and similarities. The fractal derivative is closely connected to Haussdorff’s concepts of fractional dimension geometry.
Airton Deppman, Eugenio Megías, Roman Pasechnik   +2 more
doaj   +6 more sources

FRACTAL RADIOPHYSICS. Part 3. FRACTIONAL CALCULUS IN ELECTRODYNAMICS [PDF]

Radio Physics and Radio Astronomy
Subject and Purpose. At the beginning of the 21st century, a fundamentally new scientific direction was formed, currently known as fractal radiophysics.
O. V. Lazorenko, L. F. Chernogor
doaj   +3 more sources

Electrostatics in Fractal Geometry: Fractional Calculus Approach [PDF]

Chaos, Solitons & Fractals, 2011
The electrostatics properties of composite materials with fractal geometry are studied in the framework of fractional calculus. An electric field in a composite dielectric with a fractal charge distribution is obtained in the spherical symmetry case. The
Alexander Iomin, Baskin, Bateman, Ben-Avraham, de Gennes, Emmanuel Baskin, Falconer, Gouyet, Iomin, Kolmogorov, Landau, Le Mehaute, Mandelbrot, Metzler, Metzler, Montroll, Nigmatulin, Oldham, Olemskoi, Podlubny, Ren, Samko, Stockman, Stockman, Tarasov, Tricomi, Weiss, West   +27 more
core   +2 more sources

Diffusion on Middle-ξ Cantor Sets

Entropy, 2018
In this paper, we study Cζ-calculus on generalized Cantor sets, which have self-similar properties and fractional dimensions that exceed their topological dimensions.
Alireza Khalili Golmankhaneh, Arran Fernandez, Ali Khalili Golmankhaneh, Dumitru Baleanu   +3 more
doaj   +3 more sources

Sumudu transform in fractal calculus

Applied Mathematics and Computation, 2019
The Cη-Calculus includes functions on fractal sets, which are not differentiable or integrable using ordinary calculus. Sumudu transforms have an important role in control engineering problems because of preserving units, the scaling property of domains,
A. Golmankhaneh, C. Tunç
semanticscholar   +4 more sources

Applying fractional calculus to malware spread: A fractal-based approach to threat analysis. [PDF]

PLoS One
Malware is a common word in modern era. Everyone using computer is aware of it. Some users have to face the problem known as Cyber crimes. Nobody can survive without use of modern technologies based on computer networking.
Razi N, Riaz MB, Bano A, Kamran T, Ishtiaq U, Shafiq A.   +5 more
europepmc   +2 more sources

Fractal physiology and the fractional calculus: a perspective [PDF]

Frontiers in Physiology, 2010
This paper presents a restricted overview of Fractal Physiology focusing on the complexity of the human body and the characterization of that complexity through fractal measures and their dynamics, with fractal dynamics being described by the fractional ...
Bruce J West
doaj   +3 more sources