Accurate relationships between fractals and fractional integrals: New approaches and evaluations-Reference-Cited by-同舟云学术

Accurate relationships between fractals and fractional integrals: New approaches and evaluations

Published:2017-10-01 Issue:5 Volume:20 Page:1263-1280
ISSN:1314-2224
Container-title:Fractional Calculus and Applied Analysis
language:en
Short-container-title:

Author:

Nigmatullin Raoul R.¹²,Zhang Wei³²,Gubaidullin Iskander¹

Affiliation:

1. Radioelectronic and Information-Measurements Technics Department Kazan National Research Technical University (KNRTU-KAI) Karl Marx str.10, 420011 – Kazan , Tatarstan , RUSSIAN Federation

2. JNU-KNRTU (KAI) Joint Lab. of FracDynamics and Signal Processing JiNan University (JNU) , Guangzhou , China

3. Department of Electronic Engineering College of Information Science and Technology JiNan University (JNU) Guangzhou – 510632, Guangdong , China

Abstract

Abstract In this paper the accurate relationships between the averaging procedure of a smooth function over 1D- fractal sets and the fractional integral of the RL-type are established. The numerical verifications are realized for confirmation of the analytical results and the physical meaning of these obtained formulas is discussed. Besides, the generalizations of the results for a combination of fractal circuits having a discrete set of fractal dimensions were obtained. We suppose that these new results help understand deeper the intimate links between fractals and fractional integrals of different types. These results can be used in different branches of the interdisciplinary physics, where the different equations describing the different physical phenomena and containing the fractional derivatives and integrals are used.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/fca-2017-0066/pdf

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