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Fractional Calculus in Signal, Imaging Processing and Machine Learning, 2nd...
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Fractional Calculus in Signal, Imaging Processing and Machine Learning, 2nd Edition

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "Optimization, Big Data, and AI/ML".

Deadline for manuscript submissions: closed (31 March 2026) | Viewed by 1270

Special Issue Editor

Prof. Dr. Yi-Fei Pu

E-Mail Website
Guest Editor
College of Computer Science, Sichuan University, Chengdu 610065, China
Interests: signal processing; image processing; circuits and systems; artificial intelligence
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Fractional-order intelligent information processing refers to many fields of science and engineering that incorporate fractional calculus concepts into their modeling and design. Fractional calculus is a generalization of the classical integer-order differentiation and integration theory. The theory and application of fractional calculus show that the fractional calculus operator is the best description for many complex natural or social phenomena. The fractional order can provide additional freedom of design for various applications. Due to its many unique characteristics, fractional calculus is being widely explored across many fields, such as signal and image processing, machine learning, computing law, neuromorphic computing, etc.

This Special Issue aims to further advance research on topics relating to fractional calculus in signal and image processing and machine learning. Topics for submission include (but are not limited to) the following:

  • Fractional-order signal processing;
  • Fractional-order image processing;
  • Fractional-order machine learning;
  • Fractional-order computing law;
  • Fractional-order neuromorphic computing.

Prof. Dr. Yi-Fei Pu
Guest Editor

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 250 words) can be sent to the Editorial Office for assessment.

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.

Keywords

  • fractional-order signal processing
  • fractional-order image processing
  • fractional-order machine learning
  • fractional-order computing law
  • fractional-order neuromorphic computing

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Published Papers (2 papers)

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Research

39 pages, 3506 KB  
Article
Explainable Multi-Objective Evacuation Optimization: A Fractional-Order EvoMapX Approach with Grünwald-Letnikov Memory and Fractal Landscape Analysis
by Islam S. Fathi, Ahmed R. El-Saeed, Mohammed Tawfik and Mohammed Aly
Fractal Fract. 2026, 10(5), 314; https://doi.org/10.3390/fractalfract10050314 - 6 May 2026
Viewed by 212
Abstract
Population-based metaheuristic algorithms are widely used for multi-objective city evacuation planning, yet their opaque internal dynamics limit practitioner trust in safety-critical contexts. This study introduces, to the best of our knowledge, the first unified coupling of fractional calculus and fractal analysis with the [...] Read more.
Population-based metaheuristic algorithms are widely used for multi-objective city evacuation planning, yet their opaque internal dynamics limit practitioner trust in safety-critical contexts. This study introduces, to the best of our knowledge, the first unified coupling of fractional calculus and fractal analysis with the EvoMapX process-level explainability framework in the context of evacuation optimization. In contrast with classical integer-order EvoMapX paired with exponential moving averages of operator credit, the proposed formulation embeds long-range memory directly into the explainability pipeline through Caputo and Grünwald–Letnikov derivatives. The Operator Attribution Matrix (OAM), Population Evolution Graph (PEG), and Convergence Driver Score (CDS) are extended with fractional-order formulations employing Caputo and Grünwald-Letnikov fractional derivatives with adaptive memory parameters, alongside Mittag–Leffler urgency escalation dynamics. A Fractional-Order PSO variant (FO-EPSO) with segment-specific fractional velocity updates and a fractal fitness landscape analysis module for adaptive parameter tuning are introduced. The framework incorporates nine evacuation-specific operators, a spatial OAM for zone-level attribution, and a multi-stakeholder explanation pipeline. Experiments across 520 disaster scenarios demonstrate that explainability and optimization performance are not mutually exclusive: the EvoMapX-integrated NSGA-II achieved a mean hypervolume of 0.731 versus 0.728 for the standard variant, with less than 5% computational overhead. The OAM revealed disaster-type-specific operator patterns invisible to conventional analysis. Real-world validations on Beijing Chaoyang District and Kigali, Rwanda, confirmed these findings. From an operational standpoint, the most consequential outcome of this work concerns its impact on human decision-makers: a controlled study with 45 emergency-management professionals showed that incorporating EvoMapX explanations cut the time required to commit to an evacuation plan by 24.9%, raised reported decision confidence by 20.3%, and lifted self-assessed algorithm understanding from 18.1% to 78.9% (all p < 0.001). Equally important for real-time disaster response, this entire layer of process-level transparency is delivered with a runtime penalty of under 5% relative to the non-explainable baselines, which we view as a key practical advantage for field deployment. This work establishes fractional-order process-level transparency as a feasible and beneficial paradigm for interpretable optimization in safety-critical domains. Full article
(This article belongs to the Special Issue Fractional Calculus in Signal, Imaging Processing and Machine Learning, 2nd Edition)
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23 pages, 542 KB  
Article
FAdamWav: A Fractional Wavelet Gradient Optimizer for Neural Networks
by Oscar Herrera-Alcántara, Salvador Arellano-Balderas, Sandra Rodríguez-Mondragón, José Alejandro Reyes-Ortíz and Jaime Navarro-Fuentes
Fractal Fract. 2026, 10(3), 149; https://doi.org/10.3390/fractalfract10030149 - 26 Feb 2026
Viewed by 407
Abstract
The optimizer is a critical element of neural networks because it computes their optimal parameters through a training process. The Adam optimizer is considered the state of the art in deep learning. However, a drawback is the cost of storing and computing their [...] Read more.
The optimizer is a critical element of neural networks because it computes their optimal parameters through a training process. The Adam optimizer is considered the state of the art in deep learning. However, a drawback is the cost of storing and computing their gradients. A useful tool for addressing this issue is the application of the wavelet transform, and other relevant tool is the fractional derivative, which can be used to create fractional gradient optimizers. This research combines the wavelet transform and fractional optimizers to propose FAdamWav, a fractional version of Adam that uses (i) a parametric discrete wavelet transform to theoretically save 50%, 75% or 87.5% of gradient’s memory with one, two or three transformation levels, and (ii) a fractional gradient to optimize the neural network parameters. Experiments indicate that the saved memory is lower than the theoretical bounds, but memory is saved and fractional wavelet-based optimizers have competitive performance compared to their non-fractional and non-wavelet counterparts. Full article
(This article belongs to the Special Issue Fractional Calculus in Signal, Imaging Processing and Machine Learning, 2nd Edition)
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