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.

Section
Search by Title/Keyword
 
Order results
Display
Results per page
Data-Driven Modeling, Prediction and Control of Fractional-Order Systems
edited by Fudong Ge, and
submission deadline 30 May 2026 | 1 articles | Viewed by 641 | 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 13820 | 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 | 5 articles | Viewed by 3298 | 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 790 | 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 314 | 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 | Viewed by 35 | 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 submission deadline 13 Jun 2026 | 1 articles | Viewed by 1185 | 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 | 4 articles | Viewed by 2733 | 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 | 1 articles | Viewed by 716 | 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 | 6 articles | Viewed by 5136 | 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 4340 | 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 2200 | 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 1807 | 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)
Applications of Fractal Analysis in Structural Geology
edited by , Yuhang Guo and
submission deadline 30 Jun 2026 | 1 articles | Viewed by 1000 | 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)
Fractional Differential Operators with Classical and New Memory Kernels, Second Edition submission deadline 30 Jun 2026 | 1 articles | Viewed by 644 | 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)
Fractals in Earthquake and Atmospheric Science submission deadline 30 Jun 2026 | 1 articles | Viewed by 566 | 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)
Fractional Stochastic Process: Theory and Applications submission deadline 30 Jun 2026 | Viewed by 424 | 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)
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 131 | 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)
New Horizons in Fractional and Fractal Dynamics: Unraveling Complexity in Chaotic Systems
edited by and
submission deadline 30 Jun 2026 | Viewed by 102 | 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)
Advances in Fractional-Order PID Control: Theory and Applications
edited by Jorge Mario Cruz-Duarte and César-Fernando Méndez-Barrios
submission deadline 30 Jun 2026 | Viewed by 96 | Submission Open
Keywords: fractional systems; PID control; control theory; chaotic dynamics; automatic control; real-world applications; time-delay systems
(This special issue belongs to the Section Engineering)
Multifractal Phenomena in Turbulence
edited by Alexander A. Migdal
submission deadline 30 Jun 2026 | Viewed by 88 | Submission Open
Keywords: turbulence theory; multifractal phenomena; microscopic theory; phenomenological modeling; numerical simulation; experimental validation
(This special issue belongs to the Section Complexity)
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 83 | 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)
Advances in Fractional-Order Control and Optimization for Sustainable Energy Systems
edited by and
submission deadline 30 Jun 2026 | Viewed by 53 | 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)
Fractal Geometry and Advanced Analysis in Energy Storage Systems
edited by Mei Yin and
submission deadline 30 Jun 2026 | Viewed by 40 | Submission Open
Keywords: fractional calculus; anomalous heat and mass transfer; renewable and hybrid energy systems; geothermal applications; viscoelastic modelling; computational strategies
(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 3559 | 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 2402 | 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)
Recent Computational Methods for Fractal and Fractional Nonlinear Partial Differential Equations
edited by and
submission deadline 31 Jul 2026 | 4 articles | Viewed by 3044 | 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)
Implementations and Applications of Algorithms Based on Fractional Calculus to Engineering Problems submission deadline 31 Jul 2026 | 2 articles | Viewed by 2881 | 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)
Advances in Dynamics and Control of Fractional-Order Systems
edited by Ruihong Li
submission deadline 31 Jul 2026 | 4 articles | Viewed by 1677 | 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 Analysis in Underground Engineering, Second Edition
edited by , , , , Defu Zhu and Kaijun Miao
submission deadline 31 Jul 2026 | 1 articles | Viewed by 737 | 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 418 | 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)
Applications of Fractal Interpolation in Mathematical Functions submission deadline 31 Jul 2026 | 1 articles | Viewed by 285 | 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)
Applications of Fractal Geometry in Surface Science
edited by , Glenda Quaresma Ramos and
submission deadline 31 Jul 2026 | Viewed by 104 | Submission Open
Keywords: fractal geometry; multifractals; surface roughness; biophysics; AFM/SEM/TEM in life sciences; morphological complexity; biomaterials; surface characterization; lacunarity; minkowski functionals
(This special issue belongs to the Section Life Science, Biophysics)
Modeling and Inverse Problems of Nonlocal Phenomena
edited by Philipp Zimmermann
submission deadline 1 Aug 2026 | Viewed by 40 | Submission Open
Keywords: nonlocal partial differential equations; nonlinear fractional dynamical systems; anomalous diffusion models; nonlocal operators; Runge’ s approximation; nonlocal inverse problems
(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 4178 | 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 843 | 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 180 | 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-Order Dynamics in AI: Neural Networks and Applications
edited by
submission deadline 20 Aug 2026 | Viewed by 56 | Submission Open
Keywords: fractional-order calculus; artificial intelligence; neural networks; machine learning; nonlinear dynamics; memory effects; optimisation; deep learning
(This special issue belongs to the Section Engineering)
Fractional-Order Controllers in Electronics and Automation Engineering, 2nd Edition
edited by and Joaquin Alvarez
submission deadline 30 Aug 2026 | Viewed by 9 | 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)
Fractional and Fractal Methods in Biomedical Imaging and Time Series Learning
edited by , Chengjun Wang and
submission deadline 31 Aug 2026 | 3 articles | Viewed by 2423 | 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 | 1 articles | Viewed by 740 | 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)
Hybrid Modeling Approaches: Deep Learning and Fractional Differential Equations in Complex Systems
edited by , and Andres Montoyo
submission deadline 31 Aug 2026 | 1 articles | Viewed by 396 | 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)
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 271 | 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
Fractal and Fractional Order Modeling of Real-World Phenomena
edited by
submission deadline 31 Aug 2026 | Viewed by 87 | 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 1394 | 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 59 | 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)
Fractal and Fractional in Geotechnical Engineering, Second Edition
edited by Shao-Heng He, Zhi Ding and
submission deadline 30 Sep 2026 | 1 articles | Viewed by 1145 | Submission Open
Keywords: fractal dimension; fractional-order mechanics; micro-to-Macro analysis; geomaterial; tunnel; rock; concrete; foamed light soil; bituminous mixture
(This special issue belongs to the Section Engineering)
Fractional Nonlinear Dynamics in Science and Engineering submission deadline 30 Sep 2026 | 1 articles | Viewed by 1008 | 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 324 | 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 175 | 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)
Back to TopTop