Results 11 to 20 of about 7,436,694 (204)

Generalized Convex Functions on Fractal Sets and Two Related Inequalities [PDF]

Abstract and Applied Analysis, 2014
We introduce the generalized convex function on fractal sets Rα ...
Huixia Mo, Xin Sui, Dongyan Yu
doaj   +2 more sources

Fractional Calculus of Fractal Functions on Weighted Sobolev Spaces

Fractal and Fractional
In this article, the α-fractal interpolation function fα corresponding to any function f belonging to the weighted Sobolev space Wρr,2(I) is defined. The convergence of sequences of α-fractal interpolation functions corresponding to mappings in Wρr,2(I ...
Md. Nazimul Islam, Imrul Kaish, Md. Nasim Akhtar, María A. Navascués   +3 more
doaj   +2 more sources

The Smoothness of Fractal Interpolation Functions on ℝ and on p-Series Local Fields [PDF]

Discrete Dynamics in Nature and Society, 2014
A fractal interpolation function on a p-series local field Kp is defined, and its p-type smoothness is shown by virtue of the equivalent relationship between the Hölder type space CσKp and the Lipschitz class Lipσ,Kp. The orders of the p-type derivatives
Jing Li, Weiyi Su
doaj   +2 more sources

Local $$\alpha $$-fractal interpolation function [PDF]

, 2023
Constructions of the (global) fractal interpolation functions on standard function spaces got a lot of attention in the last centuries. Motivated by the newly introduced local fractal functions corresponding to a local iterated functions system which is ...
M. A. Navascués, Banerjee, Akash, Md. Nasim Akhtar, Navascués, M. A., Akash Banerjee, Akhtar, Md. Nasim   +5 more
core   +1 more source

Fractal calculus approach to diffusion on fractal combs

, 2023
In this paper, we present a generalization of diffusion on fractal combs using fractal calculus. We introduce the concept of a fractal comb and its associated staircase function.
Alireza Khalili Golmankhaneh, Ontiveros, Lilián Aurora Ochoa, Lilián Aurora Ochoa Ontiveros, Khalili Golmankhaneh, Alireza   +3 more
core   +1 more source

Energy-optimal steering of transitions through a fractal basin boundary. [PDF]

, 2004
We study fluctuational transitions in a discrete dy- namical system having two co-existing attractors in phase space, separated by a fractal basin boundary. It is shown that transitions occur via a unique ac- cessible point on the boundary.
Luchinsky, D. G., Silchenko, A. N., McClintock, Peter V. E., Beri, S.   +3 more
core   +4 more sources

Fractal Sobolev systems of functions associated with orthonormal systems of functions [PDF]

, 2022
This paper introduces the α-fractal Sobolev system of functions corresponding to Sobolev orthonormal system of functions. An approximation-related result similar to Weierstrass theorem is derived. It is shown that the set of α-fractal versions of Sobolev
Akhtar, Md. N., Navascués, M. A., Islam, Md. N., Kaish, I., M. A. Navascués, Md. N. Islam, I. Kaish, Md. N. Akhtar   +7 more
core   +1 more source

A Finite Element Approach to Modelling Fractal Ultrasonic Transducers [PDF]

, 2014
Piezoelectric ultrasonic transducers usually employ composite structures to improve their transmission and reception sensitivities. The geometry of the composite is regular with one dominant length scale and, since these are resonant devices, this ...
Mulholland, Anthony, Algehyne, Ebrahem
core   +4 more sources

Fractal Models for SAR images [PDF]

, 2011
In this thesis the modeling of SAR (Synthetic Aperture Radar) images of natural surfaces described via fractal models is dealt with. A complete theoretical forward model linking the parameters describing the scene observed by the sensor to the stochastic
Zinno, Ivana
core   +1 more source

Analysis of a Fractal Boundary: The Graph of the Knopp Function

Abstract and Applied Analysis, 2015
A usual classification tool to study a fractal interface is the computation of its fractal dimension. But a recent method developed by Y. Heurteaux and S.
Mourad Ben Slimane, Clothilde Mélot
doaj   +1 more source