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 Mathematical Modelling: Theory, Methods and Applications
edited by Faranak Rabiei, and
submission deadline 15 May 2025 | 8 articles | Viewed by 14889 | Submission Open
Keywords: fractional differential and integral equations; new fractional operators and their properties; existence and uniqueness of solutions; analytical and numerical methods; stability analysis; fractional calculus in physics; fractional dynamics in complex systems; applications to science and engineering
(This special issue belongs to the Section Numerical and Computational Methods)
Application of Anomalous Diffusion Modeling Based on Fractal and Fractional Derivatives
edited by , Jianxiong Cao, and
submission deadline 15 May 2025 | 4 articles | Viewed by 5753 | Submission Open
Keywords: anomalous diffusion process; non-ergodic fractional dynamical systems; nonlocal and fractional models; fractional biology model; non-Gaussian noises; fractional stochastic differential equations; integral equations; finite difference methods; finite element methods; mathematical models for COVID-19; spectral methods; fractional lie symmetry; local fractional derivative
(This special issue belongs to the Section Numerical and Computational Methods)
Fractal Mechanics of Engineering Materials, 2nd Edition submission deadline 15 May 2025 | 1 articles | Viewed by 1316 | Submission Open
Keywords: fractal analysis; fractal dimension; fractal mechanics; continuum mechanics; fracture mechanics; fatigue and fatigue crack growth; damage mechanics; experimental mechanics
Distributed Control and Optimization of Fractional-Order Systems: Theory and Applications
edited by Jun Shen and Cuihong Wang
submission deadline 16 May 2025 | 1 articles | Viewed by 1219 | 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)
Application of Fractals in Complex Networks of Engineering and Medicine
edited by and
submission deadline 21 May 2025 | 5 articles | Viewed by 13222 | Submission Open
Keywords: fractals; complex networks; data mining; complex systems; chaos; engineering; medicine
(This special issue belongs to the Section Engineering)
Recent Advances in Fractional-Order Neural Networks: Theory and Application, 2nd Edition
edited by and Lulu Lu
submission deadline 25 May 2025 | 2 articles | Viewed by 2121 | 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)
Fractional Diffusion, Multistability and Control in Complex Systems
edited by Mingshu Peng
submission deadline 30 May 2025 | 4 articles | Viewed by 5927 | Submission Open
Keywords: turing instability; multistability; bifurcation; chaos; fractal differential equations; complexity; mathematical modelling; control; critical point theory; boundary value problem; stability; delay; diffusion; pattern formation; spatio-temporal behavior; related practical problem
(This special issue belongs to the Section General Mathematics, Analysis)
Analysis of Heat Conduction and Anomalous Diffusion in Fractional Calculus submission deadline 30 May 2025 | 4 articles | Viewed by 3041 | Submission Open
Keywords: fractional calculus and fractal media; thermo-molecular physics; thermodynamics; heat and mass transfer; bio-heat transfer; fractional thermal conduction; anomalous thermal diffusion; nonequilibrium processes; nonequilibrium thermodynamics; kinetics theory
(This special issue belongs to the Section Mathematical Physics)
Pore Structure and Fractal Characteristics in Unconventional Oil and Gas Reservoirs
edited by , Jizhen Zhang and Quanzhong Guan
submission deadline 31 May 2025 | 17 articles | Viewed by 18100 | Submission Open
Keywords: pore structure; pore heterogeneity; complexity; fractal characteristics; microstructures; fractal cracks
(This special issue belongs to the Section Complexity)
Fixed Point Theory and Fractals submission deadline 31 May 2025 | 6 articles | Viewed by 4940 | Submission Open
Keywords: fixed point theorems; fractal sets; functions and measures; fixed-point approximation and stability; iterative methods for the solution of differential and integral equations; iterated function systems; discrete dynamical systems; fractional calculus related to fixed point theory; dynamical systems or deterministic/stochastic fractals; applications of these fields
(This special issue belongs to the Section General Mathematics, Analysis)
Advanced Modeling and Methods of Statistical Processing of Stochastic Signals in Fractional Dynamic Systems
edited by and Jacek Leśkow
submission deadline 13 Jun 2025 | 4 articles | Viewed by 8513 | Submission Open
Keywords: fractional stochastic processes; cyclostationary random processes; fractional-order signal processing; fractional and hybrid dynamic systems; signal statistical processing techniques; fractional-order machine learning techniques in signal processing; signal computer simulation techniques
(This special issue belongs to the Section Probability and Statistics)
Numerical Analysis and Iterative Methods for Fractional Differential Equations
edited by Mudassir Shams and
submission deadline 13 Jun 2025 | Viewed by 430 | 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)
Applications of General Fractional Calculus Models: Insights into Viscoelasticity and Wave Propagation
edited by Yiying Feng, , Yiming Wang and
submission deadline 20 Jun 2025 | 5 articles | Viewed by 2444 | Submission Open
Keywords: general fractional calculus; integration of mathematics and engineering; fractional rheological models; fractal dimensional space; nonlinear theory; fractional wave propagation models
(This special issue belongs to the Section Engineering)
Symmetry and Solutions of Fractional Differential Equations with Their Developments
edited by Lihong Zhang, , and
submission deadline 30 Jun 2025 | 12 articles | Viewed by 21814 | Submission Open
Keywords: nonlinear fractional ordinary (partial) differential equations and applications; nonlinear problem involving fractional Laplacian operators and their variants; nonlinear Hammerstein equations involving fractional operators; nonlocal Monge– Ampere equation and its extensions; nonlocal operators; symmetries; and applications; geometrical methods for problems of mathematical physics; geometrical analysis and differential equations; monotonicity of solutions to various differential equations; existence and uniqueness of solutions to differential equations; symmetry of solutions to differential equations
(This special issue belongs to the Section General Mathematics, Analysis)
Fractional Systems, Integrals and Derivatives: Theory and Application submission deadline 30 Jun 2025 | 13 articles | Viewed by 14026 | Submission Open
Keywords: fractional derivatives of constant order; distributed order fractional derivative; variable order fractional derivative; fractional differential equations/systems; functional-differential equations/systems; stability analysis of fractional-order systems
(This special issue belongs to the Section General Mathematics, Analysis)
Fractal and Multifractal Analysis in Environmental, Medical and Technical Fields: Pattern Recognition, Analysis and Processing of Images submission deadline 30 Jun 2025 | 1 articles | Viewed by 2513 | Submission Open
Keywords: fractal analysis; multifractal spectrum; lacunarity spectrum; pattern recognition; neural networks; mathematical morphology; machine learning; medical images; nature textures; surfaces; scanning probe microscopy (SPM); transmission electron microscopy (TEM); scanning electron microscopy (SEM)
(This special issue belongs to the Section Life Science, Biophysics)
Fractal and Fractional in Construction Materials
edited by and
submission deadline 30 Jun 2025 | 2 articles | Viewed by 2272 | Submission Open
Keywords: construction materials; fractal and fractional; mechanical performance; fractal theory; experiment; transportation; durability
(This special issue belongs to the Section Engineering)
Advanced Fractional Sliding Mode Control for Dynamic and Robotic Systems
edited by Mehran Rahmani
submission deadline 30 Jun 2025 | 2 articles | Viewed by 2028 | Submission Open
Keywords: fractional sliding mode control; robust control; dynamic systems; robotics
(This special issue belongs to the Section Engineering)
Fractional Gravity/Cosmology in Classical and Quantum Regimes, Second Edition submission deadline 30 Jun 2025 | 1 articles | Viewed by 1737 | 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 2025 | 1 articles | Viewed by 1216 | 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)
Efficient Development of Geo-Energy and Carbon Sequestration in Fractal Geo-Systems: New Challenges
edited by Zhongwei Wu, Chuanzhi Cui and
submission deadline 30 Jun 2025 | 1 articles | Viewed by 731 | Submission Open
Keywords: geo-energy development; fractal geometry; CCUS/CCS; data analysis technology; production enhancement technologies; multi-phase flow discipline; water– rock reaction in fractal systems
(This special issue belongs to the Section Engineering)
Fractional Order Mechatronics
edited by and Pengchong Chen
submission deadline 30 Jun 2025 | Viewed by 490 | Submission Open
Keywords: fractional-order system and control; mechatronics; fractional-order modeling; application actuators and sensors; system stability and optimization
(This special issue belongs to the Section Engineering)
Feature Papers for Numerical and Computational Methods Section 2024–2025: Analog and Digital Implementations
edited by
submission deadline 30 Jun 2025 | Viewed by 234 | Submission Open
Keywords: fractional calculus; numerical methods; approximation methods; computational procedures; algorithms; digital implementation; hardware in the loop implementation; FPGA implementation; data mining with fractional calculus methods; fractional calculus with artificial intelligence applications; image/signal analyses based on fractional calculus; fuzzy fractional calculus; neural computations with fractional calculus; applications of fractional calculus in nonlinear science; applications in control; mechanics; financial mathematics; engineering; biomedicine; etc.
(This special issue belongs to the Section Numerical and Computational Methods)
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 2025 | 2 articles | Viewed by 2446 | 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 2025 | Viewed by 417 | 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)
New Insights into Random Walks and Diffusion Equations
edited by Marco Antonio Alves Da Silva, José Carlos Cressoni and
submission deadline 18 Jul 2025 | Viewed by 356 | Submission Open
Keywords: continuous-time random walks; discrete-time random walks; diffusion equations; fractional diffusion equations; anomalous diffusion; computer simulation; markovian processes; non-markovian processes
(This special issue belongs to the Section Probability and Statistics)
Complexity, Fractality and Fractional Dynamics Applied to Science and Engineering
edited by Alexandra M.S.F. Galhano, and
submission deadline 20 Jul 2025 | 10 articles | Viewed by 15792 | 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 Differential Operators and Their Applications, 2nd Edition submission deadline 25 Jul 2025 | 8 articles | Viewed by 8080 | Submission Open
Keywords: generalized derivatives; riemann– liouville; caputo derivatives; spectral theory; asymptotic theory; qualitative theory; variational theorems; applications
(This special issue belongs to the Section Numerical and Computational Methods)
Fractal Dimensions with Applications in the Real World
edited by Jun Luo, and
submission deadline 31 Jul 2025 | 5 articles | Viewed by 5910 | Submission Open
Keywords: iterated function systems; self-similar sets; self-affine sets; fractal measures; fractal graphs; beta-expansions; Hausdorff dimension; box-counting dimension; Lipschitz equivalence; topological structures
(This special issue belongs to the Section Geometry)
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 Jul 2025 | 5 articles | Viewed by 4580 | 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)
Iterative Methods in Solving Nonlinear Equations Based on Fractal and Fractional Perspective submission deadline 31 Jul 2025 | 2 articles | Viewed by 2710 | Submission Open
Keywords: iterative methods; stability theory; methods with memory; simultaneous roots; multiple roots; fractional derivatives; fractal dimension; nonlinear dynamics; mathematical modelling
(This special issue belongs to the Section General Mathematics, Analysis)
Delayed and Stochastic Fractional Order Dynamical Systems: Theory, Numerical Methods, Control, and Applications
edited by Andreas Basse-O'Connor, Ahmadreza Haghighi, and
submission deadline 31 Jul 2025 | 1 articles | Viewed by 1511 | Submission Open
Keywords: fractional calculus; delayed systems; stochastic processes; control strategies; stability analysis; signal processing; robotics; biomedical engineering; renewable energy; communication networks; economics; finance; interdisciplinary research; electrical circuits; mechanical systems; process optimization biomedical modeling
Implementations and Applications of Algorithms Based on Fractional Calculus to Engineering Problems submission deadline 31 Jul 2025 | 1 articles | Viewed by 1444 | 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)
Fractional Calculus in the Design, Control and Implementation of Complex Systems, 2nd Edition submission deadline 31 Jul 2025 | 1 articles | Viewed by 1185 | 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)
Theoretical Development and Application in Analytical and Numerical Methods for Fractional Differential Equations submission deadline 31 Jul 2025 | 1 articles | Viewed by 971 | Submission Open
Keywords: fractional differential equations; boundary value problems; fractional integrals and derivatives; fractional Partial differential equations; fixed-point theory; fractional network
(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 2025 | Viewed by 366 | 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)
Exploration and Analysis of Higher-Order Numerical Methods for Fractional Differential Equations
edited by , Changpin Li and Min Cai
submission deadline 31 Jul 2025 | 1 articles | Viewed by 325 | 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)
Advances in Dynamics and Control of Fractional-Order Systems
edited by Ruihong Li
submission deadline 31 Jul 2025 | Viewed by 202 | 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)
Advances in Fractional Initial and Boundary Value Problems submission deadline 1 Aug 2025 | 2 articles | Viewed by 838 | Submission Open
Keywords: qualitative properties of the solutions (positivity; oscillation; asymptotic behavior; stability; etc.); topological methods in differential equations and inclusions; approximation of the solutions; eigenvalue problems; variational methods; fixed point theory; critical point theory; applications to real-world phenomena
(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 2025 | 2 articles | Viewed by 1668 | 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)
Bifurcation, Chaos, and Fractals in Fractional-Order Electrical and Electronic Systems
edited by Faqiang Wang, and Hongbo Cao
submission deadline 15 Aug 2025 | 7 articles | Viewed by 13872 | 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
(This special issue belongs to the Section Complexity)
Fractional-Order Circuits, Systems, and Signal Processing, 2nd Edition submission deadline 15 Aug 2025 | 6 articles | Viewed by 7957 | Submission Open
Keywords: fractional-order analog filters; oscillators; PLLs; fractional-order filters for digital signal and image processing; fractional-order neural networks for signal processing; modeling of fractance behavior using active/passive elements; fabrication of fractance elements; fractional-order modeling of batteries; fractional-order control systems; fractional-order bioimpedance modeling
(This special issue belongs to the Section Engineering)
Contemporary Methods of Fractional Order Differential and Differential-Operator Equations submission deadline 22 Aug 2025 | 5 articles | Viewed by 3401 | Submission Open
Keywords: fractional-order PDEs; fractional-order differential operator equations; fractional-order SDEs; fractional fokker– planck equation; fractional-order systems; inverse problems for fractional-order equations; stability of fractional-order systems; applied fractional-order equations; applied fractional-order systems; determination of order(s); determination of coefficients; solution spaces; representation of solution; fundamental solution; mittag– leffler- and wright-type functions; matrix-valued mittag– leffler and Wright functions
(This special issue belongs to the Section General Mathematics, Analysis)
Fractional Order Complex Systems: Advanced Control, Intelligent Estimation and Reinforcement Learning Image Processing​ Algorithms, Second Edition
edited by , , Driss Boutat and
submission deadline 25 Aug 2025 | 1 articles | Viewed by 811 | 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)
Nonlinear Fractional Maps: Dynamics and Control
edited by Telksnys Tadas
submission deadline 25 Aug 2025 | 1 articles | Viewed by 726 | Submission Open
(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 25 Aug 2025 | 1 articles | Viewed by 259 | 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)
Fractal and Fractional Models in Soil Mechanics
edited by Yi Pik Helen Cheng and Luju Liang
submission deadline 30 Aug 2025 | 3 articles | Viewed by 1688 | Submission Open
Keywords: fractals and fragmentation; fractional-order mechanics; force network analysis; constitutive models; analytical and numerical methods; particle shape; macro- to micromechanical granular behavior; particle size effect; crushable soil mechanics; particle breakage and fragmentation; discrete element method
(This special issue belongs to the Section Engineering)
Analysis of Fractional Stochastic Differential Equations and Their Applications
edited by Zhiguo Luo and Danfeng Luo
submission deadline 31 Aug 2025 | 8 articles | Viewed by 7582 | Submission Open
Keywords: fractional differential equations; stochastic differential equations; delay differential equations; impulsive differential equations; fuzzy differential equations; stability analysis; averaging principle; controllability; averaging principle; existence or uniqueness
(This special issue belongs to the Section General Mathematics, Analysis)
Fractal and Multifractal Analysis in Econometric Models and Empirical Finance
edited by
submission deadline 31 Aug 2025 | 4 articles | Viewed by 5675 | Submission Open
Keywords: multifractal analysis; hurst exponent; multiscale analysis; financial market efficiency; empirical finance
(This special issue belongs to the Section Mathematical Physics)
Continuous/Discrete-Time Fractional Systems: Modelling, Design and Estimation submission deadline 31 Aug 2025 | 3 articles | Viewed by 5283 | 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)
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