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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Data-Driven Modeling, Prediction and Control of Fractional-Order Systems
edited by Fudong Ge, and
submission deadline 30 May 2026 | 4 articles | Viewed by 5525 | 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 | 17 articles | Viewed by 26573 | 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 Pattern Recognition—Image and Time Series Analyses—through Fractal Geometry and Complexity Theory
edited by Lucas C. Ribas, Leonardo F. S. Scabini and
submission deadline 31 May 2026 | 7 articles | Viewed by 23458 | Submission Open
Keywords: complex systems; pattern recognition; image processing; fractal descriptors; neural networks; network science
Mathematical Inequalities in Fractional Calculus and Applications, 2nd Edition
edited by and
submission deadline 31 May 2026 | 11 articles | Viewed by 13939 | Submission Open
Keywords: fractional calculus; caputo derivative; riemann-liouville derivative; discrete fractional calculus; fractals; fractional differential equations; mathematical inequalities; time scales
(This special issue belongs to the Section General Mathematics, Analysis)
Advances in Fractional Operators: Mathematical Perspectives and Multidisciplinary Applications
edited by Leandro Tavares and
submission deadline 31 May 2026 | 5 articles | Viewed by 5780 | 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)
Advances in Nonlinear Functional Analysis on Fractional Differential Equations, 2nd Edition
edited by
submission deadline 31 May 2026 | 4 articles | Viewed by 5143 | 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)
Fractal Analysis in Unconventional Reservoirs: Theory and Applications submission deadline 31 May 2026 | 7 articles | Viewed by 5068 | 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)
Mathematical and Computational Approaches to Fractal and Fractional Systems Using Fixed Point Theory submission deadline 31 May 2026 | 5 articles | Viewed by 3938 | 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)
Fractals in Reservoir Engineering
edited by Rodolfo Camacho-Velazquez, Kouqi Liu and
submission deadline 31 May 2026 | Viewed by 307 | 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 | 5 articles | Viewed by 4059 | 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 | 11 articles | Viewed by 9906 | Submission Open
Keywords: pore structure; pore heterogeneity; complexity; fractal characteristics; microstructures; fractal cracks
(This special issue belongs to the Section Engineering)
Time-Fractal and Fractional Models in Physics and Engineering
edited by Kyungsik Kim
submission deadline 15 Jun 2026 | 7 articles | Viewed by 6501 | Submission Open
Keywords: fractals; multifractals; MDFA; MDCCA; fractional analysis; thermodynamics; statistical mechanics; machine learning; artificial intelligence; complex network; image recognition; fluid climate and global change; econophysics; brain network
(This special issue belongs to the Section Complexity)
Exploration and Analysis of Higher-Order Numerical Methods for Fractional Differential Equations
edited by , Changpin Li and Min Cai
submission deadline 15 Jun 2026 | 3 articles | Viewed by 4491 | Submission Open
Keywords: the modeling of fractional differential equations; finite difference methods for fractional differential equations; finite element methods for fractional differential equations; spectral methods for fractional differential equations; the construction of higher-order numerical differential formulas for fractional derivatives
(This special issue belongs to the Section Numerical and Computational Methods)
Fractional Mathematical Modelling: Theory, Methods, and Applications—2nd Edition
edited by and
submission deadline 16 Jun 2026 | 3 articles | Viewed by 2765 | 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 | 11 articles | Viewed by 16559 | 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)
Numerical and Exact Methods for Nonlinear Differential Equations and Applications in Physics, 2nd Edition
edited by
submission deadline 30 Jun 2026 | 10 articles | Viewed by 13816 | Submission Open
Keywords: fractional calculus; special functions in fractional calculus; mathematical modelling in physics; nonlinear models in mathematical physics; dynamics of physical systems; numerical solutions; exact solutions; soliton theory; computational physics; multiplicative calculus; fuzzy differential calculus; stochastic differential equations
(This special issue belongs to the Section Mathematical Physics)
Applications of Fractional Calculus in Modern Mathematical Modeling submission deadline 30 Jun 2026 | 8 articles | Viewed by 10162 | Submission Open
Keywords: fractional calculus; fractional differential equations (FDEs); fractional delay differential equations (FDDEs); stochastic fractional delay differential equations (SFDDEs); memory effects; fractional partial differential equations (FRDE's); stochastic fractional partial differential equations (SFPDEs); existence and uniqueness of solutions for FDEs; stability analysis of FDEs; sufficient conditions for solvability of FDEs with multi-point type data; uniqueness of solution for FDEs with impulses given by functions with several variables; solvability of functional FDES in involving P-Laplacian; multiplicity results for singular FDES in biological models; numerical methods in fractional calculus; biological systems modeling through fractional calculus; efficient computational methods to solve fractional differential equations for biological systems; control theory; mathematical modeling in finance through fractional calculus; data-driven approaches through fractional calculus; machine learning with fractional operators; future research directions and open problems in the application of fractional calculus in mathematical modeling
(This special issue belongs to the Section Numerical and Computational Methods)
Fractional Order Systems with Application to Electrical Power Engineering, 3rd Edition submission deadline 30 Jun 2026 | 8 articles | Viewed by 7530 | Submission Open
Keywords: fractional order system; distributed energy resources; energy storage system; multi-energy systems; power electronic systems; power converters; renewable energy systems; artificial intelligence; stability analysis; intelligent control; fractional calculus; reliability and resiliency
(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 7267 | 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)
Fractals in Earthquake and Atmospheric Science submission deadline 30 Jun 2026 | 6 articles | Viewed by 5266 | 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)
Multi-Scale and Fractal Research on Advanced Manufacturing and Tribology
edited by and
submission deadline 30 Jun 2026 | 3 articles | Viewed by 3695 | 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)
Mathematical and Numerical Analysis of Fractional Evolution Equations and Applications submission deadline 30 Jun 2026 | 3 articles | Viewed by 3171 | Submission Open
Keywords: fractional PDEs; numerical solutions; exact solutions; fractional Sobolev spaces; distributed parameter systems; solitary and travelling waves
(This special issue belongs to the Section Numerical and Computational Methods)
Fractional Calculus in the Design, Control and Implementation of Complex Systems, 2nd Edition submission deadline 30 Jun 2026 | 1 articles | Viewed by 2773 | 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 1906 | 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)
New Horizons in Fractional and Fractal Dynamics: Unraveling Complexity in Chaotic Systems
edited by and
submission deadline 30 Jun 2026 | 2 articles | Viewed by 1845 | 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 Control and Optimization for Sustainable Energy Systems
edited by and
submission deadline 30 Jun 2026 | 1 articles | Viewed by 1652 | 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)
Fractional Stochastic Process: Theory and Applications submission deadline 30 Jun 2026 | 1 articles | Viewed by 1602 | 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)
Fractional Differential Operators with Classical and New Memory Kernels, Second Edition submission deadline 30 Jun 2026 | 1 articles | Viewed by 1408 | 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)
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 | 1 articles | Viewed by 1257 | 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 PID Control: Theory and Applications
edited by and César-Fernando Méndez-Barrios
submission deadline 30 Jun 2026 | Viewed by 533 | 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)
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 376 | 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)
Multifractal Phenomena in Turbulence
edited by Alexander A. Migdal
submission deadline 30 Jun 2026 | Viewed by 326 | Submission Open
Keywords: turbulence theory; multifractal phenomena; microscopic theory; phenomenological modeling; numerical simulation; experimental validation
(This special issue belongs to the Section Complexity)
Fractal and Fractional Modelling Applied to Energy Storage
edited by Mei Yin and
submission deadline 30 Jun 2026 | Viewed by 243 | 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)
Numerical Solution and Applications of Fractional Differential Equations, 3rd Edition
edited by , and
submission deadline 10 Jul 2026 | 9 articles | Viewed by 8956 | Submission Open
Keywords: numerical methods; mathematical modelling; fractional calculus; fractional differential equations; numerical analysis; fast algorithm
(This special issue belongs to the Section Numerical and Computational Methods)
Recent Advances in Fractional-Order Neural Networks: Theory and Application, 2nd Edition
edited by and Lulu Lu
submission deadline 10 Jul 2026 | 3 articles | Viewed by 5255 | Submission Open
Keywords: fractional calculus; dynamics analysis; biological nervous system; circuit design and simulation; artificial intelligence
(This special issue belongs to the Section General Mathematics, Analysis)
Applications of Fractional-Order Grey Models, 2nd Edition
edited by and Shuli Yan
submission deadline 15 Jul 2026 | 5 articles | Viewed by 7416 | Submission Open
Keywords: fractional-order; grey model; prediction; algorithm; application
(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 5088 | 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)
Modelling and Analysis of Fractional Behaviours: Alternative Approaches and Characterization
edited by
submission deadline 15 Jul 2026 | Viewed by 497 | Submission Open
Keywords: fractional behaviours; modelling; non-singular kernels; fractal
(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 | 5 articles | Viewed by 5826 | 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)
Chaotic and Fractal Approaches with AI for Multidisciplinary Modeling and Applications submission deadline 20 Jul 2026 | 1 articles | Viewed by 1213 | Submission Open
Keywords: chaos theory; fractals; artificial intelligence (AI); neural networks; hybrid AI approaches; chaotic neural networks; fractional calculus; engineering applications
(This special issue belongs to the Section Optimization, Big Data, and AI/ML)
Fractional Calculus and Nonlinear Analysis: Theory and Applications submission deadline 31 Jul 2026 | 7 articles | Viewed by 14825 | 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 Dynamics and Control of Fractional-Order Systems
edited by Ruihong Li
submission deadline 31 Jul 2026 | 15 articles | Viewed by 9588 | 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)
Analysis of Geological Pore Structure Based on Fractal Theory
edited by Wei Yang and
submission deadline 31 Jul 2026 | 7 articles | Viewed by 6717 | Submission Open
Keywords: fractal theory; fractal analysis; multifractal theory; multifractal analysis; pore structure; pore– crack observation; pore connectivity
(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 | 5 articles | Viewed by 6300 | 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 | 3 articles | Viewed by 4922 | 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)
Applications of Fractal Analysis in Underground Engineering, Second Edition
edited by , , , , Defu Zhu and Kaijun Miao
submission deadline 31 Jul 2026 | 5 articles | Viewed by 4364 | 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)
Recent Advances in Fractional Differential Equations and Their Applications, 3rd Edition
edited by Xiaoli Chen, and Ting Gao
submission deadline 31 Jul 2026 | 3 articles | Viewed by 3219 | Submission Open
Keywords: nonlocal differential equations; fractional differential equations; stochastic differential equations; numerical method; machine learning methods
(This special issue belongs to the Section Numerical and Computational Methods)
Applications of Fractal Interpolation in Mathematical Functions submission deadline 31 Jul 2026 | 3 articles | Viewed by 2226 | 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)
Fractal Analysis and Data-Driven Complex Systems submission deadline 31 Jul 2026 | 3 articles | Viewed by 1476 | Submission Open
Keywords: fractal geometry; multifractal analysis; fractional brownian motion; time-series analysis; scaling laws and self-similarity
(This special issue belongs to the Section Complexity)
Fractional Dynamics Systems: Modeling, Forecasting, and Control
edited by Seenith Sivasundaram, and
submission deadline 31 Jul 2026 | 2 articles | Viewed by 1186 | Submission Open
Keywords: fractional-order systems; modeling and simulation; fractional-order control; stability and controllability; applications in engineering; biology; and finance; non-local dynamics
(This special issue belongs to the Section General Mathematics, Analysis)
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