Special Issues

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 policies 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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Fractional-Order Modeling and Control for Complex Dynamic Systems: Methodologies and Applications
edited by Necdet Sinan Özbek, and
submission deadline 30 Apr 2026 | Viewed by 288 | Submission Open
Keywords: fractional-order systems; fractional calculus; complex dynamic systems; fractional-order control; non-integer order modeling; robust control; adaptive control; sliding mode control; stability analysis; system identification; memory and hereditary systems; numerical methods for fractional systems; networked and distributed systems; machine learning in fractional control; biomedical applications of fractional models; energy systems modeling; optimization in fractional-order systems; time-domain and frequency-domain analysis
(This special issue belongs to the Section Engineering)
Fractional Differential Equations: Computation and Modelling with Applications, 2nd Edition
edited by Rajarama Mohan Jena and
submission deadline 30 Apr 2026 | Viewed by 245 | Submission Open
Keywords: fractional derivatives and integrals; fractional operators; fractal– fractional derivatives and integrals; mathematical modelling; computational efficient methods; uncertainty and artificial intelligence; non-singular kernels
New Perspectives and Applications of Fractional Order Modeling in Energy Systems submission deadline 30 Apr 2026 | Viewed by 85 | Submission Open
Keywords: fractional order differential equations; fractional modeling; fractional dynamics; anomalous transport; thermal memory effects; multiscale energy systems; fractional simulation; numerical algorithms in fractional calculus
(This special issue belongs to the Section Engineering)
Fractal Dimension Analysis in Brain Function: From Basic Mechanisms to Clinical Frontiers
edited by
submission deadline 1 May 2026 | Viewed by 156 | Submission Open
Keywords: innovative methods for FD extraction and analysis in neural signals; FD-driven improvements in BCI design and decoding strategies; personalised neuromodulation by tailoring NIBS interventions using FD metrics; FD as a non-invasive biomarker for early diagnosis and monitoring of neurological and psychiatric disorders; multimodal and cross-modal applications combining FD with EEG; MEG; fMRI; and TMS; new theoretical frameworks linking brain criticality; fractal geometry; and functional connectivity
(This special issue belongs to the Section Life Science, Biophysics)
Distributed Control and Optimization of Fractional-Order Systems: Theory and Applications
edited by Jun Shen and Cuihong Wang
submission deadline 16 May 2026 | 1 articles | Viewed by 1462 | Submission Open
Keywords: fractional-order systems; fractional-order nonlinear systems; control theory and control engineering; optimal control; distributed control; multi-agent systems; cyber-physical systems; stability of dynamic systems
(This special issue belongs to the Section Engineering)
Fractal Dynamics of Complex Systems in Society and Behavioral Science
edited by and Mingshu Peng
submission deadline 20 May 2026 | Viewed by 83 | Submission Open
Keywords: fractal dynamics; scale free; collective behavior; self-organization; adaptive and intelligent systems
(This special issue belongs to the Section Life Science, Biophysics)
Data-Driven Modeling, Prediction and Control of Fractional-Order Systems
edited by Fudong Ge, and
submission deadline 30 May 2026 | Viewed by 299 | Submission Open
Keywords: fractional-order systems; fractional-order ODE systems; fractional-order PDE systems; data-driven modeling and identification; data-driven learning and prediction; data-driven controller design; artificial intelligence/machine learning
(This special issue belongs to the Section Optimization, Big Data, and AI/ML)
Analysis and Numerical Computations of Nonlinear Fractional and Classical Differential Equations
edited by , Wenxue Zhou, Sunil Dutt Purohit, and Ahmed Refaie Ali
submission deadline 31 May 2026 | 13 articles | Viewed by 11480 | Submission Open
Keywords: nonlinear PDEs; fractional PDEs; general fractional PDEs; fractional mathematical models; mathematical models in real-world problems; integral transforms for nonlinear problems; special functions; computational methods; numeral methods; traveling wave solutions; similarity solution; series expansion method; finite element method; finite difference method; group analysis; reduced differential transform method; differential transform method; residual power series method; homotopy analysis method; decomposition method; homotopy perturbation method; asymptotic perturbation solution; variational iteration method; coupling methods
(This special issue belongs to the Section Numerical and Computational Methods)
Advances in Fractional Operators: Mathematical Perspectives and Multidisciplinary Applications
edited by Leandro Tavares and
submission deadline 31 May 2026 | 4 articles | Viewed by 2383 | Submission Open
Keywords: fractional equations; fractional operators; critical point theory; variational methods; fractional derivatives; Ψ -Hilfer fractional derivative; Mittag-Leffler function; generalized Mittag-Leffler function
(This special issue belongs to the Section General Mathematics, Analysis)
Mathematical and Computational Approaches to Fractal and Fractional Systems Using Fixed Point Theory submission deadline 31 May 2026 | 1 articles | Viewed by 539 | Submission Open
Keywords: fixed points; contraction mappings; fractal analysis; integral equations; fractional differential equations; optimization; topological spaces; decision making; best proximity points; stability analysis; image processing; fuzzy metric spaces; mathematical modeling
(This special issue belongs to the Section General Mathematics, Analysis)
Fractal Analysis in Unconventional Reservoirs: Theory and Applications submission deadline 31 May 2026 | Viewed by 226 | Submission Open
Keywords: fractal models for quantifying pore size distribution and surface roughness; multiscale pore structure analysis using fractal theory; fractal-based permeability and fluid flow simulation in low-permeability; correlation between fractal dimensions and reservoir properties (e.g.; porosity; oiliness); machine learning integrated with fractal analysis for reservoir classification and evaluation; fractal characterization of diagenetic processes and their impact on pore evolution; application of fractal theory in enhanced oil recovery (EOR) techniques for unconventional resources
(This special issue belongs to the Section Engineering)
Fractals in Reservoir Engineering
edited by Rodolfo Camacho-Velazquez
submission deadline 31 May 2026 | Submission Open
Keywords: fractal distributions; fractal parameters; petrophysical properties; fluid flow in fractal porous media; fractal partial differential equations; fractional differential equations
(This special issue belongs to the Section Engineering)
Numerical Analysis and Iterative Methods for Fractional Differential Equations
edited by Mudassir Shams and
submission deadline 13 Jun 2026 | 1 articles | Viewed by 1042 | Submission Open
Keywords: fractional differential equations; fractional-order differential equations; nonlinear fractional equations; fuzzy fractional differential equations; numerical methods and computational techniques; stability and consistency; local and global convergence; iterative methods; dynamical behaviors; topological methods; hybrid block methods; comparative analysis; error analysis and adaptive methods; applications of fractional differential equations in systems and signal processing; applications of nonlinear fractional equations in physics; biology; and engineering
(This special issue belongs to the Section Numerical and Computational Methods)
Pore Structure and Fractal Characteristics in Unconventional Oil and Gas Reservoirs, 2nd Edition
edited by , Jizhen Zhang and
submission deadline 15 Jun 2026 | 3 articles | Viewed by 1596 | Submission Open
Keywords: pore structure; pore heterogeneity; complexity; fractal characteristics; microstructures; fractal cracks
(This special issue belongs to the Section Engineering)
Fractional Mathematical Modelling: Theory, Methods, and Applications—2nd Edition
edited by and
submission deadline 16 Jun 2026 | Viewed by 281 | Submission Open
Keywords: fractional mathematical modeling; fractional differential and integral equations; novel fractional-order operators and their properties; existence and uniqueness of solutions; analytical techniques for fractional systems; numerical methods and computational algorithms; stability and control of fractional-order systems; real-world applications across science and engineering; integration with machine learning; stochastic analysis; and hybrid modeling; interdisciplinary modeling of complex systems
(This special issue belongs to the Section Numerical and Computational Methods)
Fractional Order Complex Systems: Advanced Control, Intelligent Estimation and Reinforcement Learning Image Processing​ Algorithms, Second Edition
edited by , , Driss Boutat and
submission deadline 25 Jun 2026 | 5 articles | Viewed by 3706 | Submission Open
Keywords: image processing; image fusion; image denoising; stability of fractional systems; control of fractional systems; singular fractional systems
(This special issue belongs to the Section Engineering)
Fractional Gravity/Cosmology in Classical and Quantum Regimes, Second Edition submission deadline 30 Jun 2026 | 2 articles | Viewed by 3621 | Submission Open
Keywords: fractional calculus; fractional derivatives; riesz fractional operator; caputo fractional operator; fractional Brownian motion; levy path integrals; fractional-action-like variational approach; fractional quantum mechanics; fractional classical cosmology; fractional quantum cosmology; non-local operators
(This special issue belongs to the Section Mathematical Physics)
Multi-Scale and Fractal Research on Advanced Manufacturing and Tribology
edited by and
submission deadline 30 Jun 2026 | 2 articles | Viewed by 1955 | Submission Open
Keywords: manufacturing; rough surfaces; fractal method; multi-scale approach; tribology; contact mechanics; wear; friction; lubrication
(This special issue belongs to the Section Engineering)
Fractional Calculus in the Design, Control and Implementation of Complex Systems, 2nd Edition submission deadline 30 Jun 2026 | 1 articles | Viewed by 1644 | Submission Open
Keywords: fractional calculus; chaotic systems; complex networks; variable order calculus; mathematical modeling; control theory; complexity; circuit implementation; chaos-based cryptography; neural networks; identification and modeling; signal processing; complexity measures; chaos theory; applied mathematics
(This special issue belongs to the Section Complexity)
Fractional Differential Operators with Classical and New Memory Kernels, Second Edition submission deadline 30 Jun 2026 | 1 articles | Viewed by 453 | Submission Open
Keywords: fractional operators; memory kernels; biomechanical and medical models; heat and mass transfer; analysis; special functions; and kernels; numerical and computational methods; analytical solution methods: exact and approximate; modeling approaches with nonlocal (fractional) operators; probability and statistics based on nonlocal approaches; mathematical physics: heat; mass; and momentum transfer; engineering applications and image processing; life science; biophysics; and complexity
(This special issue belongs to the Section General Mathematics, Analysis)
Fractional Stochastic Process: Theory and Applications submission deadline 30 Jun 2026 | Viewed by 271 | Submission Open
Keywords: classic and quantum mechanics; equilibrium and non-equilibrium; fluids; granular and soft matter; fractional calculus in statistical mechanics; fractional calculus in statistical physics; interdisciplinary statistical mechanics; interdisciplinary statistical physics; fault diagnosis; life prediction; signals processing; neuronal signal analysis (EEG; BCI); mathematical modeling of diseases
(This special issue belongs to the Section Probability and Statistics)
Applications of Fractal Analysis in Structural Geology
edited by , Yuhang Guo and
submission deadline 30 Jun 2026 | Viewed by 178 | Submission Open
Keywords: fractal geometry; structural complexity; scale invariance; fracture network modeling; seismic attribute analysis; reservoir heterogeneity; rock physics/seismic modeling; rock physics/seismic inversion; geomechanical prediction; digital geology; multiscale characterization; planetary geomorphology
(This special issue belongs to the Section Engineering)
Fractals in Earthquake and Atmospheric Science submission deadline 30 Jun 2026 | Viewed by 141 | Submission Open
Keywords: fractals; self-organised systems; non-linear dynamics and chaos; radon; electromagnetism; geodesy; urban air pollution; earthquakes; modelling and simulation; data analysis: algorithms and implementation
(This special issue belongs to the Section Mathematical Physics)
Computational and Analytical Approaches in Fractional Calculus for Big Data and Digital Twins
edited by , Maria Fernanda Pires da Costa and
submission deadline 30 Jun 2026 | Viewed by 91 | Submission Open
Keywords: fractional calculus; fractional differential equations; computational modeling; numerical methods; machine learning; big data; digital twins; engineering; physics
(This special issue belongs to the Section Optimization, Big Data, and AI/ML)
Complexity, Fractality and Fractional Dynamics Applied to Science and Engineering, 2nd Edition
edited by Alexandra M. S. F. Galhano, and
submission deadline 30 Jun 2026 | Viewed by 58 | Submission Open
Keywords: fractional-order systems; memory; econophysics; time series; finance; economics; big data; complex systems; biosystems; fractals
(This special issue belongs to the Section Complexity)
New Horizons in Fractional and Fractal Dynamics: Unraveling Complexity in Chaotic Systems
edited by and
submission deadline 30 Jun 2026 | Viewed by 57 | Submission Open
Keywords: fractional-order systems; stability analysis; fractional-order control theory; high-dimensional fractional-fractal simulation; chaotic time series analysis; machine learning for fractional chaos; fractal network dynamics; biological oscillator modeling; economic fractal models; security encryption applications
(This special issue belongs to the Section Complexity)
Multifractal Phenomena in Turbulence
edited by Alexander A. Migdal
submission deadline 30 Jun 2026 | Viewed by 49 | Submission Open
Keywords: turbulence theory; multifractal phenomena; microscopic theory; phenomenological modeling; numerical simulation; experimental validation
(This special issue belongs to the Section Complexity)
Advances in Fractional-Order Control and Optimization for Sustainable Energy Systems
edited by and
submission deadline 30 Jun 2026 | Viewed by 35 | Submission Open
Keywords: fractional-order control; fractional calculus; robust control; adaptive control; nonlinear systems; stability analysis; real-time applications
(This special issue belongs to the Section Engineering)
Recent Advances in Fractional-Order Equations and Their Applications in Modern Energy Systems
edited by Zhe Gao, Xiaoting Gao and Enchang Cui
submission deadline 15 Jul 2026 | 2 articles | Viewed by 3317 | Submission Open
Keywords: fractional-order control theory in modern energy systems; theoretical frameworks and foundations of fractional-order equations in modern energy systems; fractional-order modeling and analysis of modern energy systems; fractional-order control systems and implementation of modern energy systems; applications of fractional-order equations in renewable energy sources; fractional-order control and optimization of energy systems; fractional-order dynamics in energy storage and energy conversion systems; case studies and implementations of fractional-order models in energy systems; energy storage systems; supercapacitors and batteries; and hybrid energy storage
(This special issue belongs to the Section Engineering)
Recent Developments in Multidimensional Fractional Differential Equations and Fractional Difference Equations
edited by and
submission deadline 18 Jul 2026 | 3 articles | Viewed by 1661 | Submission Open
Keywords: fractional calculus; fractional differential equations; fractional difference equations; multidimensional fractional calculus; multidimensional fractional differential equations; multidimensional partial fractional differential equations; theory and applications
(This special issue belongs to the Section General Mathematics, Analysis)
Implementations and Applications of Algorithms Based on Fractional Calculus to Engineering Problems submission deadline 31 Jul 2026 | 2 articles | Viewed by 2486 | Submission Open
Keywords: fractional calculus; fractional-order systems; algorithm implementation; algorithm development; signal processing; image processing; fault detection
(This special issue belongs to the Section Engineering)
Recent Computational Methods for Fractal and Fractional Nonlinear Partial Differential Equations
edited by and
submission deadline 31 Jul 2026 | 3 articles | Viewed by 2091 | Submission Open
Keywords: fractal and fractional nonlinear partial differential equations; fractal and fractional calculus; mathematical physics; fractal variational principle
(This special issue belongs to the Section Mathematical Physics)
Applications of Fractal Analysis in Underground Engineering, Second Edition
edited by , , , , Defu Zhu and Kaijun Miao
submission deadline 31 Jul 2026 | 1 articles | Viewed by 589 | Submission Open
Keywords: fractal analysis; fractal characteristics; data fractal processing; rock mechanics; rock engineering; under engineering; water/gas/heat conduction; joints; fractures and voids; fluid migration; chaos and roughness; image processing process; entropy
(This special issue belongs to the Section Engineering)
Advances in Fractional Dynamics: Computational Approaches and Applications in Cosmology, Mechanics, and Complex Systems
edited by
submission deadline 31 Jul 2026 | Viewed by 389 | Submission Open
Keywords: fractional calculus; fractional dynamics; fractional differential equations; cosmology; gravitational systems; particle motion; classical and quantum mechanics; emergent structures in nonlinear and multifractal regimes; complex systems
(This special issue belongs to the Section Mathematical Physics)
Advances in Dynamics and Control of Fractional-Order Systems
edited by Ruihong Li
submission deadline 31 Jul 2026 | Viewed by 337 | Submission Open
Keywords: complex dynamical behaviors; bifurcation analysis; stability analysis; resonance analysis; chaos synchronization; control strategies; system identification
(This special issue belongs to the Section Engineering)
Applications of Fractal Interpolation in Mathematical Functions submission deadline 31 Jul 2026 | Viewed by 142 | Submission Open
Keywords: fractal interpolation functions (FIFs); fractal functions and surfaces; iterated function systems (IFS); self-similarity and nonlinearity; self-affine and self-conformal structures; fractal approximation and modeling; function approximation; irregular and complex data modeling; signal and image processing; data fitting and curve reconstruction; mathematical and computational algorithms; applications in engineering; finance; biology; and natural sciences; multifractal analysis; function spaces and interpolation theory; fractal geometry in applied mathematics
(This special issue belongs to the Section General Mathematics, Analysis)
Recent Advances in Nonlocal Problems Involving the Fractional Laplacian Operators
edited by
submission deadline 14 Aug 2026 | 5 articles | Viewed by 3536 | Submission Open
Keywords: fractional differential equations; fractional Sobolev spaces; variable exponent elliptic operator; fractional Laplacian problems with the external magnetic field; variational methods on the existence and multiplicity of solutions; a  priori estimates and existence of solutions; uniqueness; non-existence; classifications of solutions; critical point theorem on the existence and multiplicity of solutions
(This special issue belongs to the Section General Mathematics, Analysis)
Stochastic Dynamical Systems with Fractional Derivative: Theoretical Analysis and Numerical Simulation
edited by and
submission deadline 15 Aug 2026 | 1 articles | Viewed by 681 | Submission Open
Keywords: fractional calculus; fractional integration; fractional derivative; stochastic dynamical systems; stabilization; system response; fractional-order controller
(This special issue belongs to the Section Engineering)
Fractional Calculus, Artificial Intelligence and Complexity Analysis in Neurological and Chaotic Systems
edited by , Jorge Mario Cruz-Duarte, Milan Stehlik and
submission deadline 15 Aug 2026 | Viewed by 100 | Submission Open
Keywords: fractional calculus; neurological systems; artificial intelligence; chaotic dynamics; fractal dimension; entropy measures; EEG/ECoG signal processing; neuroimaging analysis; time series analysis; brain complexity
Fractional and Fractal Methods in Biomedical Imaging and Time Series Learning
edited by , Chengjun Wang and Jiabao Li
submission deadline 31 Aug 2026 | 1 articles | Viewed by 505 | Submission Open
Keywords: fractional calculus; medical robotic control; biomedical signal processing; medical image analysis; time series machine learning
(This special issue belongs to the Section Optimization, Big Data, and AI/ML)
Analysis and Applications of Fractional Calculus in Computational Physics submission deadline 31 Aug 2026 | Viewed by 375 | Submission Open
Keywords: fractional calculus in physics; fractional operators; integral transformations of irrational functions; inverse Laplace transform of irrational functions; time-delayed fractional models; numerical methods in fractional problems
(This special issue belongs to the Section Mathematical Physics)
Bifurcation, Chaos, and Fractals in Fractional-Order Electrical and Electronic Systems, 2nd Edition
edited by Faqiang Wang, and Hongbo Cao
submission deadline 31 Aug 2026 | Viewed by 206 | Submission Open
Keywords: bifurcation and its control chaos and its control; fractals and their control; fractional-order inductor/capacitor; fractional-order memristor/meminductor/memcapacitor; fractional-order circuits and systems; fractional-order electrical and electronic systems; multi-timescale and entropy analysis; fractional calculus applications
Hybrid Modeling Approaches: Deep Learning and Fractional Differential Equations in Complex Systems
edited by , and Andres Montoyo
submission deadline 31 Aug 2026 | Viewed by 146 | Submission Open
Keywords: fractional differential equations (FDEs); fractional difference equations; fractional physics-informed neural networks (fPINNs); deep learning for dynamical systems; Fourier neural operators (FNOs); nonlocal and memory-dependent models; variable-order differential equations; fractal-fractional order mathematical models; time-fractional and space-fractional models; hybrid neural– stochastic modeling; inverse problems in fractional systems; reinforcement learning in fractional systems; cognitive modeling with FDEs; multiscale modeling in complex systems; deep neural network solvers for FDEs; applications in biology and neuroscience; computational and stability methods in fractional calculus
(This special issue belongs to the Section Optimization, Big Data, and AI/ML)
Fractal and Fractional Order Modeling of Real-World Phenomena
edited by
submission deadline 31 Aug 2026 | Viewed by 52 | Submission Open
Keywords: Mandelbrot's fractals; discrete difference equations; fractional order continuous differential equations; mathematical modeling; real-world systems; continuous and discrete models; fractional calculus
(This special issue belongs to the Section General Mathematics, Analysis)
Fractal Theory and Models in Nonlinear Dynamics and Their Applications, 2nd Edition submission deadline 15 Sep 2026 | 2 articles | Viewed by 1079 | Submission Open
Keywords: fractal theory; multifractals; fractal– fractional calculus; fractional chaotic systems; fractional nonlinear dynamics
(This special issue belongs to the Section Mathematical Physics)
Continuous/Discrete-Time Fractional Systems: Modelling, Design and Estimation, 2nd Edition submission deadline 15 Sep 2026 | Viewed by 31 | Submission Open
Keywords: autoregressive-moving average (ARMA); shift-invariant; scale-invariant; fBm; Liouville; Liouville– Caputo; Hadamard; Riemann– Liouville; Dzherbashian– Caputo; Grunwald– Letnikov; two-sided Riesz– Feller derivatives
(This special issue belongs to the Section General Mathematics, Analysis)
Fractional Nonlinear Dynamics in Science and Engineering submission deadline 30 Sep 2026 | 1 articles | Viewed by 828 | Submission Open
Keywords: nonlinear fractional models; deterministic and stochastic models; fractional nonlinear systems; dynamics of fractional nonlinear systems; complex systems
(This special issue belongs to the Section General Mathematics, Analysis)
Calculus of Variations, Fractional Calculus and Their Applications
edited by
submission deadline 30 Sep 2026 | Viewed by 299 | Submission Open
Keywords: fractional calculus of variations; fractional derivatives and integrals; necessary and sufficient optimality conditions; fractional Euler– Lagrange equation; numerical and analytical methods; applications of fractional calculus of variations
(This special issue belongs to the Section General Mathematics, Analysis)
Fractional Calculus in Bioengineering and Mathematical Biology: Novel Approaches to Biomedical Applications and Infectious Disease Dynamics
edited by
submission deadline 30 Sep 2026 | Viewed by 101 | Submission Open
Keywords: fractional dynamics; bioengineering; biomedical applications; epidemic modeling; mathematical biology; fractional differential equations; computational modeling; anomalous diffusion; memory effects in biology
(This special issue belongs to the Section Life Science, Biophysics)
Fractal Approaches and Machine Learning in Financial Markets
edited by
submission deadline 30 Sep 2026 | Viewed by 43 | Submission Open
Keywords: fractal and multifractal analysis; machine learning; deep learning; financial market; volatility; risk management; portfolio optimization; asset pricing; financial decision-making
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