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Fractal and Fractional publishes Special Issues to create collections of papers on specific topics, with the aim of building a community of authors and readers to discuss the latest research and develop new ideas and research directions. Special Issues are led by Guest Editors, who are experts on the topic and all Special Issue submissions follow MDPI's standard editorial process. The journal’s Editor-in-Chief and/or designated Editorial Board Member will oversee Guest Editor appointments and Special Issue proposals, checking their content for relevance and ensuring the suitability of the material for the journal. The papers published in a Special Issue will be collected and displayed on a dedicated page of the journal’s website. Further information on MDPI's Special Issue polices and Guest Editor responsibilities can be found here. For any inquiries related to a Special Issue, please contact the Editorial Office.

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Complex Dynamics and Multifractal Analysis of Financial Markets

edited by Leonardo Henrique Silva Fernandes and

Benjamin Miranda Tabak

submission deadline 31 Dec 2024 | 1 articles | Viewed by 1932 | Submission Open

Keywords: complexity; cross-correlations; financial markets; multifractality; time series

(This special issue belongs to the Section Probability and Statistics)

Anomalous Diffusion and Relaxations in Liquid Crystals: Fractal and Fractional Behavior

edited by Rafael Soares Zola and

Ervin K. Lenzi

submission deadline 31 Dec 2024 | 1 articles | Viewed by 1412 | Submission Open

Keywords: anomalous diffusion; non-Debye relaxation; modulated liquid crystal phases; coarsening dynamics; pattern formation; fractal and fractional calculus; anomalous scaling; memory effects

(This special issue belongs to the Section Complexity)

Fractional Calculus Operators and the Mittag-Leffler Function, 2nd Edition

edited by

Maja Andrić

submission deadline 31 Dec 2024 | 1 articles | Viewed by 993 | Submission Open

Keywords: fractional calculus; mittag-Leffler function; fractional integral operator; integral inequality; convex function; bound of operator

(This special issue belongs to the Section General Mathematics, Analysis)

Recent Research in Fractional-Order Controllers: Selected Papers from the ICMASC’24

edited by

Carla M. A. Pinto

Cristina I. Muresan

and

Dana Copot

submission deadline 31 Dec 2024 | Viewed by 558 | Submission Open

Keywords: fractional-order control; FOPID; fractional calculus; modelling; implementation; stability analysis; control design

Fractional Order Systems: Deterministic and Stochastic Analysis, 3rd Edition

edited by

Amar Debbouche

submission deadline 31 Dec 2024 | Viewed by 254 | Submission Open

Keywords: fractional dynamical systems; fractional inverse problems; fractional mathematical models; fractional PDEs; fractional operators

Fractal Geometry and Dynamical Systems

edited by

Mrinal Kanti Roychowdhury

and Saurabh Verma

submission deadline 31 Dec 2024 | Viewed by 152 | Submission Open

Keywords: iterated function systems; julia and mandelbrot sets; self-similar sets and measures; self-affine and self-conformal sets/measures; fractal interpolation functions; quantization dimension; box dimension; hausdorff dimension and Lq dimensions

(This special issue belongs to the Section Geometry)

Current Trends on Fractional-Order Systems: Bifurcations, Synchronization, and Chaos

edited by Joaquin Alvarez and J. Pena-Ramirez

submission deadline 15 Jan 2025 | Viewed by 376 | Submission Open

Keywords: stability; oscillators; complex networks; chaos; bifurcation; synchronization; emergent behavior; fractional order neural networks

(This special issue belongs to the Section Complexity)

Fractal and Fractional in Geomaterials, 2nd Edition

edited by Yifei Sun

submission deadline 15 Jan 2025 | Viewed by 262 | Submission Open

Keywords: fractal media; fractional mechanics; micro-to-macro. geomaterials; nonconventional approach

(This special issue belongs to the Section Engineering)

New Trends on Generalized Fractional Calculus, 2nd Edition

edited by

Milton Ferreira

Maria Manuela Fernandes Rodrigues

and

Nelson Felipe Loureiro Vieira

submission deadline 15 Jan 2025 | Viewed by 148 | Submission Open

Keywords: generalised fractional calculus; fractional calculus with general analytic kernels; ψ -fractional derivatives; weighted fractional derivatives; integral transforms; special functions; fractional inequalities; fractional ODE and PDE; initial and Boundary value problems

(This special issue belongs to the Section Numerical and Computational Methods)

Advances in Pattern Recognition—Image and Time Series Analyses—through Fractal Geometry and Complexity Theory

edited by Lucas C. Ribas, Leonardo F. S. Scabini and

Pier Luigi Gentili

submission deadline 17 Jan 2025 | 3 articles | Viewed by 3341 | Submission Open

Keywords: complex systems; pattern recognition; image processing; fractal descriptors; neural networks; network science

Fractional-Order Learning Systems: Theory, Algorithms, and Emerging Applications

edited by

Sayed Pouria Talebi

submission deadline 20 Jan 2025 | Viewed by 146 | Submission Open

Keywords: fractional-order learning systems; fractional-order calculus; signal processing; information processing; machine learning; control agorithms; modern circuits

(This special issue belongs to the Section Optimization, Big Data, and AI/ML)

Fractal Theory Applications in the Contact Interface of Mechanical Equipment

edited by Shuangfu Suo, Min Huang and Qi An

submission deadline 25 Jan 2025 | 1 articles | Viewed by 458 | Submission Open

Keywords: fractal theory; contact interface; contact mechanics; surface topography; tribological properties; cross-scale

(This special issue belongs to the Section Engineering)

Fractal Analysis and Its Applications in Rock Engineering

edited by

Lihai Tan

Xiaohan Yang

and Gaofeng Liu

submission deadline 31 Jan 2025 | 11 articles | Viewed by 11864 | Submission Open

Keywords: fractal analysis and modeling; fragmentation; rock mechanics; rock fractures; rock microstructures; rock engineering ; geomechanical processes; engineering application

(This special issue belongs to the Section Engineering)

Fractional-Order Chaotic System: Control and Synchronization, 2nd Edition

edited by

Song Zheng

Emad E. Mahmoud

and

Yangquan Chen

submission deadline 31 Jan 2025 | 6 articles | Viewed by 7539 | Submission Open

Keywords: fractional-order; complex systems; chaos; synchronization; control; stabilization; consensus; identification; modelling

(This special issue belongs to the Section Complexity)

Fractional Calculus and Nonlinear Analysis: Theory and Applications

edited by

Wei-Shih Du

Marko Kostić

and

Daniel Velinov

submission deadline 31 Jan 2025 | 4 articles | Viewed by 5899 | Submission Open

Keywords: fractional differential equation; fractional complicated system; fractional operator; modeling biological phenomena; nonlinear dynamics and chaos; fixed point theory; optimization; critical point theory; optimization; convex analysis

(This special issue belongs to the Section General Mathematics, Analysis)

Advances in Fractional-Order Chaotic and Complex Systems

edited by

Chunhua Wang

Fei Yu

and

Wei Yao

submission deadline 31 Jan 2025 | 1 articles | Viewed by 1631 | Submission Open

Keywords: fractional-order theory; fractional-order systems; complex systems; chaos; chaotic systems; chaos applications; non-linear systems; neural networks

(This special issue belongs to the Section Complexity)

Metric Spaces with Its Application to Fractional Differential Equations

edited by Khurram Shabbir, Monica-Felicia Bota and

Liliana Guran

submission deadline 14 Feb 2025 | 6 articles | Viewed by 7766 | Submission Open

Keywords: metric spaces; fixed points theorems; well-posedness; stability; fractional differential equations with different kernels; fractal patterns; statistical convergence; decision making problems; numerical and computational methods; mathematical physics; mathematics in biology; intuitionistic fuzzy relations

(This special issue belongs to the Section General Mathematics, Analysis)

Fractional Elliptic and Parabolic Equations: Analysis and Related Topics

edited by Wenxiong Chen and Leyun Wu

submission deadline 14 Feb 2025 | 1 articles | Viewed by 803 | Submission Open

Keywords: fractional elliptic equations; fractional parabolic equations; fractional laplacian; non-local operators; variational method; multiplicity numerical analysis; applications of fractional equations; nonlinearity; symmetry; monotonicity; a priori estimate; existence; non-existence; uniqueness; classification; method of moving planes; sliding method; etc.

(This special issue belongs to the Section General Mathematics, Analysis)

Fractional Differential Equations: Computation and Modelling with Applications

edited by

Rajarama Mohan Jena

and

Snehashish Chakraverty

submission deadline 20 Feb 2025 | 9 articles | Viewed by 11842 | Submission Open

Keywords: fractional derivatives and integrals; fractional operators; fractal-fractional derivatives and integrals; mathematical modelling; computational efficient methods; uncertainty and artificial intelligence; nonsingular kernels

(This special issue belongs to the Section General Mathematics, Analysis)

Applications of Fractional-Order Calculus in Robotics, 2nd Edition

edited by

Abhaya Pal Singh

and

Kishore Bingi

submission deadline 20 Feb 2025 | Viewed by 193 | Submission Open

Keywords: fractional calculus; fractional control; fractional modeling; robotics; fractal manipulators

Advances in Fractional Order Systems and Robust Control, 2nd Edition

edited by

Feng Liu

submission deadline 21 Feb 2025 | 4 articles | Viewed by 3087 | Submission Open

Keywords: fractional order systems; fractional differential equations; robust control; fractional controllers; stability analysis; modeling

(This special issue belongs to the Section Engineering)

Numerical Solution and Applications of Fractional Differential Equations, 2nd Edition

edited by

Libo Feng

Yang Liu

and

Lin Liu

submission deadline 25 Feb 2025 | 7 articles | Viewed by 6473 | Submission Open

Keywords: numerical methods; mathematical modeling; fractional calculus; fractional differential equations; numerical analysis; fast algorithm

(This special issue belongs to the Section Numerical and Computational Methods)

Recent Advances in Fractional Fourier Transforms and Applications, 2nd Edition

edited by

Zunwei Fu

Bingzhao Li

and

Xiangyang Lu

submission deadline 25 Feb 2025 | 2 articles | Viewed by 1227 | Submission Open

Keywords: fractional Fourier transform; linear canonical transform; digital signal processing; fractional integral operator; partial differential equations

(This special issue belongs to the Section General Mathematics, Analysis)

Mathematical and Physical Analysis of Fractional Dynamical Systems

edited by Dimplekumar Chalishajar and Kasinathan Ravikumar

submission deadline 28 Feb 2025 | 10 articles | Viewed by 11309 | Submission Open

Keywords: functional differential and integral systems with applications; fractional PDE with applications; fractional numerical analysis and numerical simulations; oscillation/nonoscillation; feedback control and various stability analysis; boundary value problems; Markov chain process; jump processes; coupled dynamics; fractional processes; space-time fractional equations; fractional Brownian motion and Rosenblatt process; long-range dependence; time– space fractional vibration equation; convergence; eigenvalue; green function

(This special issue belongs to the Section Engineering)

Women’s Special Issue Series: Fractal and Fractional, 2nd Edition

edited by

Ivanka Stamova

Carla M. A. Pinto

and

Dana Copot

submission deadline 28 Feb 2025 | 3 articles | Viewed by 3477 | Submission Open

Keywords: fractals and fractional calculus; fractals and fractional calculus in computing; fractals and fractional calculus in mathematical physics; fractals and fractional calculus in biology and neurocomputing; fractals and fractional calculus in engineering; fractals and fractional calculus in economics; fratals and fractional calculus in educational technologies; fractional calculus and control; fractional calculus and optimization; fractional calculus and stability; fractional models and uncertainty; related fractional modeling

(This special issue belongs to the Section Complexity)

Fractal and Multifractal Analysis in Econometric Models and Empirical Finance

edited by

Sun-Yong Choi

submission deadline 28 Feb 2025 | 2 articles | Viewed by 2548 | Submission Open

Keywords: multifractal analysis; hurst exponent; multiscale analysis; financial market efficiency; empirical finance

(This special issue belongs to the Section Mathematical Physics)

Fractals in Biophysics and Their Applications

edited by Anirban Bandyopadhyay

submission deadline 28 Feb 2025 | 3 articles | Viewed by 2301 | Submission Open

Keywords: quantum mechanics; quantum biology; biophysics; biophotonics; bioelectronics; neuroscience; brain dynamics; fractal analysis in medicine; water network in biology

(This special issue belongs to the Section Life Science, Biophysics)

Advanced Research in Fractal Properties of Nanoparticle and Its Application

edited by

Ivana Stajcic

and Aleksandar P. Stajčić

submission deadline 28 Feb 2025 | 1 articles | Viewed by 1085 | Submission Open

Keywords: fractal dimension; surface– property relation; nanoparticles and composites; surface– synthesis/dispersion relation; grain boundary

(This special issue belongs to the Section Mathematical Physics)

Mathematical Description of Human Nervous System Using Fractals, Fractional and Integer Order Calculus

edited by

Stefan Balint

submission deadline 28 Feb 2025 | Viewed by 180 | Submission Open

Keywords: human nervous system; mathematical description using fractals; mathematical description using integer order and fractional order calculus

(This special issue belongs to the Section Life Science, Biophysics)

Applications of Fractional-Order Grey Models

edited by Shuli Yan and

Lifeng Wu

submission deadline 14 Mar 2025 | 8 articles | Viewed by 8477 | Submission Open

Keywords: fractional-order; grey model; prediction; algorithm; application

(This special issue belongs to the Section Engineering)

Advances in Fractional-Order Control with Special Focus to Power Systems

edited by

Martin Čech

submission deadline 14 Mar 2025 | Viewed by 168 | Submission Open

Keywords: fractional-order controllers; fractional-order PID controllers; fractional-order systems; adaptive fractional-order control; robust control; advanced process control; power systems; control performance assessment; system identification

(This special issue belongs to the Section Engineering)

Advances in Fractional-Order Multiagent Systems: Theory and Applications

edited by Ping Gong

submission deadline 15 Mar 2025 | 7 articles | Viewed by 9592 | Submission Open

Keywords: fractional-order dynamics; multiagent systems; distributed coordination control; nonlinear control; stability analysis; algorithm design

(This special issue belongs to the Section Engineering)

Applications of Fractional-Order Systems to Automatic Control

edited by

Germán Ardúl Muñoz Hernández

and

Fermi Guerrero-Castellanos

submission deadline 15 Mar 2025 | 6 articles | Viewed by 8813 | Submission Open

Keywords: unmanned vehicles; renewable energy; electric power; manufacturing; robotics; automotive control systems; time-delay systems; modeling and control of complex systems

(This special issue belongs to the Section Engineering)

Fractional Porous Medium Type and Related Equations

edited by Petra Wittbold

submission deadline 15 Mar 2025 | Viewed by 90 | Submission Open

Keywords: time-fractional porous medium and related equations; subdiffusion processes; memory effects; stochastic perturbation; numerical approximation

(This special issue belongs to the Section General Mathematics, Analysis)

Advances in Fractional Order Derivatives and Their Applications, 3rd Edition

edited by

Sameerah Jamal

submission deadline 20 Mar 2025 | Viewed by 120 | Submission Open

Keywords: fractional order derivatives; fractional calculus; Caputo derivatives; Riemann– Liouville derivatives; numerical analysis; modeling; application

(This special issue belongs to the Section Numerical and Computational Methods)

Advances in Nonlinear Functional Analysis on Fractional Differential Equations, 2nd Edition

edited by

Bipan Hazarika

submission deadline 20 Mar 2025 | Viewed by 97 | Submission Open

Keywords: nonlinear functional analysis; control theory and applications; nonlinear fractional dynamic equations on timescale; fixed point theory; ecological systems; nonlinear dynamical systems; fractional calculus; solvability of infinite systems; sequence spaces and function spaces; nonlinear functionals and variational methods; nonlinear operators

(This special issue belongs to the Section General Mathematics, Analysis)

Fracture Analysis of Materials Based on Fractal Nature

edited by

Luis Eduardo Kosteski

, Leandro Ferreira Friedrich and

Jie Xu

submission deadline 25 Mar 2025 | 1 articles | Viewed by 1253 | Submission Open

Keywords: size effect; fracture; damage; experimental analysis; acoustic emission; numerical simulations

(This special issue belongs to the Section Engineering)

Fractal Analysis and Fractal Dimension in Materials Chemistry, 2nd Edition

edited by

Gianina Dobrescu

Florica Papa

and

Razvan State

submission deadline 25 Mar 2025 | Viewed by 135 | Submission Open

Keywords: fractal dimension; fractal adsorption isotherms; catalysis; diffusion-limited reactions; fractions

Fractional-Order in Modeling and Control of Power Electronic-Based Systems

edited by

Ton Duc Do

and

Duy Truong Duong

submission deadline 25 Mar 2025 | Viewed by 54 | Submission Open

Keywords: power converter; digital control; model-based control; data-based control; data-driven control; modelling; fractional order

(This special issue belongs to the Section Engineering)

Fractional- and Integer-Order System: Control Theory and Applications, 2nd Edition

edited by

Thach Ngoc Dinh

Shyam Kamal

Rajesh Kumar Pandey

, Bijnan Bandyopadhyay and

Jun Huang

submission deadline 31 Mar 2025 | 3 articles | Viewed by 3109 | Submission Open

(This special issue belongs to the Section Engineering)

Biocomplexity and Fractal Analysis: Theory and Applications

edited by

Annamaria Zaia

and

Pierluigi Maponi

submission deadline 31 Mar 2025 | 1 articles | Viewed by 1332 | Submission Open

Keywords: biocomplexity; fractal analysis; biomathematical modeling; computer-aided diagnosis; biomarker; computational tools; biomedical imaging

(This special issue belongs to the Section Complexity)

Analysis and Applications of Fractional Calculus and Mathematical Modelling

edited by

Marcelo Kaminski Lenzi

submission deadline 31 Mar 2025 | 1 articles | Viewed by 932 | Submission Open

Keywords: fractional calculus; fractional differential and integral equations; fractional models; mathematical modelling; fractional dynamics; modeling simulation; process control; application of fractional calculus; focusing on modeling and optimization.

(This special issue belongs to the Section General Mathematics, Analysis)

New Advances and Applications of Fractional Oscillate System

edited by Liang Wang

submission deadline 31 Mar 2025 | Viewed by 382 | Submission Open

Keywords: fractional calculus; fractional-order oscillate systems; stochastic dynamical systems; vibro-impact system; stochastic bifurcation and chaos

(This special issue belongs to the Section Engineering)

Fractal Analysis in Biology and Medicine

edited by

Ivan Zaletel

submission deadline 1 Apr 2025 | Viewed by 393 | Submission Open

Keywords: fractal analysis; fractal dimension; complexity; self-similarity; neuroscience; morphometry; cell and tissue analysis

Fractional-Order Dynamics and Control in Green Energy Systems

edited by Manashita Borah and

Christos Volos

submission deadline 18 Apr 2025 | 3 articles | Viewed by 2398 | Submission Open

Keywords: fractional-order chaos; energy storage systems; dynamics; control systems; energy storage systems; biological systems; renewable energy applications; energy-efficient robots; green transportation

(This special issue belongs to the Section Engineering)

Advances in Boundary Value Problems for Fractional Differential Equations, 3rd Edition

edited by

Rodica Luca

submission deadline 20 Apr 2025 | 1 articles | Viewed by 366 | Submission Open

Keywords: fractional differential equations; fractional differential inclusions; fractional differential inequalities; initial value problems; boundary value problems; existence and nonexistence; uniqueness and multiplicity; stability; numerical computations

(This special issue belongs to the Section General Mathematics, Analysis)

Applications of Fractals and Fractional Calculus in Nuclear Reactors

edited by Gilberto Espinosa Paredes and Carlos Antonio Cruz-López

submission deadline 25 Apr 2025 | Submission Open

Keywords: Nuclear Reactor analysis; fractal mathematical modeling; fractional mathematical modeling; fractional compartmental models; Mittag-Leffler kernel; stability analysis; semi-analytical method; analytical and numerical methods; symmetry analysis and conservation laws; numerical and computational methods

(This special issue belongs to the Section Mathematical Physics)

Fractional-Order Controllers in Electronics and Automation Engineering

edited by

Allan G. Soriano-Sánchez

and Didier López-Mancilla

submission deadline 30 Apr 2025 | 3 articles | Viewed by 4198 | Submission Open

Keywords: fractional-order calculus; fractional-order control; fractional-order approximations; fractional-order implementation tuning of; fractional-order controllers

(This special issue belongs to the Section Engineering)

Enhancing Pain Assessment and Anesthesia Management: Fractional Modeling with AI

edited by

Martine Neckebroek

submission deadline 30 Apr 2025 | 1 articles | Viewed by 503 | Submission Open

Keywords: anesthesia and fractional calculus and AI; pain and fractional calculus and AI; neuro monitoring; fractional calculus

(This special issue belongs to the Section Life Science, Biophysics)

Fractal Analysis and Its Applications in Materials Science

edited by

Zine El Abiddine Fellah

submission deadline 30 Apr 2025 | Viewed by 195 | Submission Open

Keywords: fractal analysis; fractal materials; fractals media; metamaterial characterization; acoustic characterization; porous materials; micropolar materials; poroelastic /elastic materials; solid and fluid mechanics; self-similar media; fractal analysis and applications in materials science

(This special issue belongs to the Section Engineering)

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