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Fractal Fract
Special Issues
New Aspects of Local Fractional Calculus
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New Aspects of Local Fractional Calculus

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "General Mathematics, Analysis".

Deadline for manuscript submissions: closed (15 April 2021) | Viewed by 5743

Special Issue Editors

Dr. Dimiter Prodanov

E-Mail Website
Chief Guest Editor
1. EHS and NERF, Interuniversity Microelectronics Center (imec), 3001 Leuven, Belgium
2. IICT, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria
Interests: fractional calculus; local fractional calculus; computer algebra tools; numerical techniques; special functions; modeling of biophysical phenomena; image processing.
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Dumitru Baleanu

grade E-Mail Website
Guest Editor
1. Institute of Space Sciences, P.O. Box MG-23, RO-077125 Magurele-Bucharest, Romania
2. Department of Mathematics, Cankaya University, Ankara 06530, Turkey
Interests: fractional dynamics; fractional differential equations; discrete mathematics; fractals; image processing; bio-informatics; mathematical biology; soliton theory; Lie symmetry; dynamic systems on time scales; computational complexity; the wavelet method
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Interest in fractal and non-differentiable functions was rekindled with the works of Mandelbrot in fractals, where such fractal objects were used to model natural phenomena, such as the coast of Britain. In the broad sense of understanding, local fractional calculus evolved from several distinct perspectives: firstly, this was the study of localized versions of the classical fractional derivatives; secondly, it was formulated in terms of difference quotients defined as fractional velocities, with physical applications in mind; and thirdly, it was developed as an extension of the ordinary calculus for functions defined on Cantor sets. The local fractional calculus can be used to characterize the growth of singular functions, and it was applied to problems in stochastic mechanics and in general to strongly non-linear phenomena, which are difficult to describe through smooth mathematical objects.

We invite and welcome review, expository, and original research articles dealing with the recent advances in the theory of local fractional derivatives on Cantor sets, fractional velocities, fractal integral operators, and their multidisciplinary applications.

Dr. Dimiter Prodanov
Prof. Dr. Dumitru Baleanu
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fractal and Fractional is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2700 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Published Papers (2 papers)

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Research

21 pages, 1002 KiB  
Article
Continuity Result on the Order of a Nonlinear Fractional Pseudo-Parabolic Equation with Caputo Derivative
by Ho Duy Binh, Luc Nguyen Hoang, Dumitru Baleanu and Ho Thi Kim Van
Fractal Fract. 2021, 5(2), 41; https://0-doi-org.brum.beds.ac.uk/10.3390/fractalfract5020041 - 05 May 2021
Cited by 4 | Viewed by 2305
Abstract
In this paper, we consider a problem of continuity fractional-order for pseudo-parabolic equations with the fractional derivative of Caputo. Here, we investigate the stability of the problem with respect to derivative parameters and initial data. We also show that [...] Read more.
In this paper, we consider a problem of continuity fractional-order for pseudo-parabolic equations with the fractional derivative of Caputo. Here, we investigate the stability of the problem with respect to derivative parameters and initial data. We also show that uω′→uω in an appropriate sense as ω′→ω, where ω is the fractional order. Moreover, to test the continuity fractional-order, we present several numerical examples to illustrate this property. Full article
(This article belongs to the Special Issue New Aspects of Local Fractional Calculus)
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17 pages, 342 KiB  
Article
Generalized Differentiability of Continuous Functions
by Dimiter Prodanov
Fractal Fract. 2020, 4(4), 56; https://0-doi-org.brum.beds.ac.uk/10.3390/fractalfract4040056 - 10 Dec 2020
Viewed by 1952
Abstract
Many physical phenomena give rise to mathematical models in terms of fractal, non-differentiable functions. The paper introduces a broad generalization of the derivative in terms of the maximal modulus of continuity of the primitive function. These derivatives are called indicial derivatives. As an [...] Read more.
Many physical phenomena give rise to mathematical models in terms of fractal, non-differentiable functions. The paper introduces a broad generalization of the derivative in terms of the maximal modulus of continuity of the primitive function. These derivatives are called indicial derivatives. As an application, the indicial derivatives are used to characterize the nowhere monotonous functions. Furthermore, the non-differentiability set of such derivatives is proven to be of measure zero. As a second application, the indicial derivative is used in the proof of the Lebesgue differentiation theorem. Finally, the connection with the fractional velocities is demonstrated. Full article
(This article belongs to the Special Issue New Aspects of Local Fractional Calculus)
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