A fractional calculus on arbitrary time scales: Fractional differentiation and fractional integration

Nadia Benkhettou; Artur M.C. Brito da Cruz; Delfim F.M. Torres

首页> 外文期刊>Signal processing >A fractional calculus on arbitrary time scales: Fractional differentiation and fractional integration

【24h】

A fractional calculus on arbitrary time scales: Fractional differentiation and fractional integration

机译：任意时间尺度上的分数演算：分数微分和分数积分

获取原文

获取原文并翻译 | 示例

掌桥外文数据库（机构版） >>

开具论文收录证明 >>

文献代查 >>

页面导航

摘要
著录项
相似文献
相关主题

摘要

We introduce a general notion of fractional (noninteger) derivative for functions defined on arbitrary time scales. The basic tools for the time-scale fractional calculus (fractional differentiation and fractional integration) are then developed. As particular cases, one obtains the usual time-scale Hilger derivative when the order of differentiation is one, and a local approach to fractional calculus when the time scale is chosen to be the set of real numbers.

机译：对于在任意时标上定义的函数，我们引入了分数（非整数）导数的一般概念。然后开发了用于时标分数微积分（分数微分和分数积分）的基本工具。在特定情况下，当微分的阶次为1时，可获得通常的时标Hilger导数；而当将时标选择为实数集时，则可获得分数微积分的局部方法。

著录项

来源
《Signal processing》 |2015年第2期|230-237|共8页
作者
Nadia Benkhettou; Artur M.C. Brito da Cruz; Delfim F.M. Torres;
展开▼
作者单位

Laboratoire de Mathematiques, Universite de SidiBel-Abbes, B.P. 89, 22000 Sidi Bel-Abbes, Algerie;

Escola Superior de Tecnologia de Setubal, Estefanilha, 2910-761 Setubal, Portugal,Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal;

Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal;

展开▼
收录信息
原文格式 PDF
正文语种 eng
中图分类
关键词
Fractional differentiation; Fractional integration; Calculus on time scales;

机译：分数微分;小数积分;时间尺度上的微积分;

相似文献

外文文献
中文文献
专利

1. Fractal-fractional differentiation and integration: Connecting fractal calculus and fractional calculus to predict complex system [J] . Atangana Abdon Chaos, Solitons and Fractals: Applications in Science and Engineering: An Interdisciplinary Journal of Nonlinear Science . 2017,第期

机译：分形分数分化和集成：连接分形微积分和分数微积分预测复杂系统
2. An Approach to Fractional Differential Geometry and Fractal Space-Time via Fractional Calculus for Non-Differentiable Functions [J] . Guy Jumarie International journal of theoretical physics, group theory, and nonlinear optics . 2015,第3期

机译：非可微分函数分数微积分的分数微分几何和分形空间的方法
3. A conformable fractional calculus on arbitrary time scales [J] . Nadia Benkhettou, Salima Hassani, Delfim F.M. Torres Journal of King Saud University . 2016,第1期

机译：任意时间尺度上的合格分数演算
4. GEOMETRIC INTERPRETATION OF DISCRETE FRACTIONAL ORDER CONTROLLERS BASED ON SAMPLING TIME SCALING PROPERTY AND EXPERIMENTAL VERIFICATION OF FRACTIONAL 1/S~α SYSTEMS' ROBUSTNESS [C] . Chengbin Ma, Yoichi Hori 19th Biennial Conference on Mechanical Vibration and Noise . 2003

机译：基于采样时间尺度特性和分数1 / S〜α系统稳健性的实验验证的离散分数阶控制器的几何解释
5. Fractional Angular Momentum and the Application of the Fractional Calculus to Quantum Mechanics [D] . Bildstein, Steven Bentley. 2019

机译：分数角动量及其在微积分学中的应用
6. Analytical Solutions for Multi-Time Scale Fractional Stochastic Differential Equations Driven by Fractional Brownian Motion and Their Applications [O] . Xiao-Li Ding, Juan J. Nieto 2018

机译：分数褐色运动及其应用驱动的多时间尺度分数随机微分方程的分析解
7. A Fractional Calculus on Arbitrary Time Scales: Fractional Differentiation and Fractional Integration∗† [O] . Nadia Benkhettou, Delfim F. M. Torres 2016

机译：任意时间尺度的分数微分：分数微分和分数积分*†

A fractional calculus on arbitrary time scales: Fractional differentiation and fractional integration

摘要

著录项

相似文献

相关主题

期刊订阅