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 polices and Guest Editor responsibilities can be found here. For any inquiries related to a Special Issue, please contact the Editorial Office.

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Recent Advances in the Equation with Nonlinear Fractional Diffusion
edited by Armando Gallegos and
submission deadline 31 Dec 2024 | 2 articles | Viewed by 2134 | Submission Open
(This special issue belongs to the Section General Mathematics, Analysis)
Complex Dynamics and Multifractal Analysis of Financial Markets
edited by Leonardo Henrique Silva Fernandes and
submission deadline 31 Dec 2024 | 1 articles | Viewed by 1906 | Submission Open
Keywords: complexity; cross-correlations; financial markets; multifractality; time series
(This special issue belongs to the Section Probability and Statistics)
Anomalous Diffusion and Relaxations in Liquid Crystals: Fractal and Fractional Behavior
edited by Rafael Soares Zola and
submission deadline 31 Dec 2024 | 1 articles | Viewed by 1388 | Submission Open
Keywords: anomalous diffusion; non-Debye relaxation; modulated liquid crystal phases; coarsening dynamics; pattern formation; fractal and fractional calculus; anomalous scaling; memory effects
(This special issue belongs to the Section Complexity)
Fractional Calculus Operators and the Mittag-Leffler Function, 2nd Edition
edited by
submission deadline 31 Dec 2024 | 1 articles | Viewed by 958 | Submission Open
Keywords: fractional calculus; mittag-Leffler function; fractional integral operator; integral inequality; convex function; bound of operator
(This special issue belongs to the Section General Mathematics, Analysis)
Recent Research in Fractional-Order Controllers: Selected Papers from the ICMASC’24 submission deadline 31 Dec 2024 | Viewed by 554 | Submission Open
Keywords: fractional-order control; FOPID; fractional calculus; modelling; implementation; stability analysis; control design
Fractional Order Systems: Deterministic and Stochastic Analysis, 3rd Edition
edited by
submission deadline 31 Dec 2024 | Viewed by 246 | Submission Open
Keywords: fractional dynamical systems; fractional inverse problems; fractional mathematical models; fractional PDEs; fractional operators
Fractal Geometry and Dynamical Systems
edited by and Saurabh Verma
submission deadline 31 Dec 2024 | Viewed by 150 | Submission Open
Keywords: iterated function systems; julia and mandelbrot sets; self-similar sets and measures; self-affine and self-conformal sets/measures; fractal interpolation functions; quantization dimension; box dimension; hausdorff dimension and Lq dimensions
(This special issue belongs to the Section Geometry)
Current Trends on Fractional-Order Systems: Bifurcations, Synchronization, and Chaos
edited by Joaquin Alvarez and J. Pena-Ramirez
submission deadline 15 Jan 2025 | Viewed by 373 | Submission Open
Keywords: stability; oscillators; complex networks; chaos; bifurcation; synchronization; emergent behavior; fractional order neural networks
(This special issue belongs to the Section Complexity)
Fractal and Fractional in Geomaterials, 2nd Edition
edited by Yifei Sun
submission deadline 15 Jan 2025 | Viewed by 257 | Submission Open
Keywords: fractal media; fractional mechanics; micro-to-macro. geomaterials; nonconventional approach
(This special issue belongs to the Section Engineering)
New Trends on Generalized Fractional Calculus, 2nd Edition submission deadline 15 Jan 2025 | Viewed by 136 | Submission Open
Keywords: generalised fractional calculus; fractional calculus with general analytic kernels; ψ -fractional derivatives; weighted fractional derivatives; integral transforms; special functions; fractional inequalities; fractional ODE and PDE; initial and Boundary value problems
(This special issue belongs to the Section Numerical and Computational Methods)
Advances in Pattern Recognition—Image and Time Series Analyses—through Fractal Geometry and Complexity Theory
edited by Lucas C. Ribas, Leonardo F. S. Scabini and
submission deadline 17 Jan 2025 | 3 articles | Viewed by 3278 | Submission Open
Keywords: complex systems; pattern recognition; image processing; fractal descriptors; neural networks; network science
Fractional-Order Learning Systems: Theory, Algorithms, and Emerging Applications submission deadline 20 Jan 2025 | Viewed by 141 | Submission Open
Keywords: fractional-order learning systems; fractional-order calculus; signal processing; information processing; machine learning; control agorithms; modern circuits
(This special issue belongs to the Section Optimization, Big Data, and AI/ML)
Fractal Theory Applications in the Contact Interface of Mechanical Equipment
edited by Shuangfu Suo, Min Huang and Qi An
submission deadline 25 Jan 2025 | 1 articles | Viewed by 336 | Submission Open
Keywords: fractal theory; contact interface; contact mechanics; surface topography; tribological properties; cross-scale
(This special issue belongs to the Section Engineering)
Fractal Analysis and Its Applications in Rock Engineering
edited by , and Gaofeng Liu
submission deadline 31 Jan 2025 | 11 articles | Viewed by 11713 | Submission Open
Keywords: fractal analysis and modeling; fragmentation; rock mechanics; rock fractures; rock microstructures; rock engineering  ; geomechanical processes; engineering application
(This special issue belongs to the Section Engineering)
Fractional-Order Chaotic System: Control and Synchronization, 2nd Edition submission deadline 31 Jan 2025 | 5 articles | Viewed by 7242 | Submission Open
Keywords: fractional-order; complex systems; chaos; synchronization; control; stabilization; consensus; identification; modelling
(This special issue belongs to the Section Complexity)
Fractional Calculus and Nonlinear Analysis: Theory and Applications submission deadline 31 Jan 2025 | 4 articles | Viewed by 5862 | Submission Open
Keywords: fractional differential equation; fractional complicated system; fractional operator; modeling biological phenomena; nonlinear dynamics and chaos; fixed point theory; optimization; critical point theory; optimization; convex analysis
(This special issue belongs to the Section General Mathematics, Analysis)
Advances in Fractional-Order Chaotic and Complex Systems
edited by , and
submission deadline 31 Jan 2025 | 1 articles | Viewed by 1610 | Submission Open
Keywords: fractional-order theory; fractional-order systems; complex systems; chaos; chaotic systems; chaos applications; non-linear systems; neural networks
(This special issue belongs to the Section Complexity)
Metric Spaces with Its Application to Fractional Differential Equations
edited by Khurram Shabbir, Monica-Felicia Bota and
submission deadline 14 Feb 2025 | 6 articles | Viewed by 7718 | Submission Open
Keywords: metric spaces; fixed points theorems; well-posedness; stability; fractional differential equations with different kernels; fractal patterns; statistical convergence; decision making problems; numerical and computational methods; mathematical physics; mathematics in biology; intuitionistic fuzzy relations
(This special issue belongs to the Section General Mathematics, Analysis)
Fractional Elliptic and Parabolic Equations: Analysis and Related Topics
edited by Wenxiong Chen and Leyun Wu
submission deadline 14 Feb 2025 | 1 articles | Viewed by 794 | Submission Open
Keywords: fractional elliptic equations; fractional parabolic equations; fractional laplacian; non-local operators; variational method; multiplicity numerical analysis; applications of fractional equations; nonlinearity; symmetry; monotonicity; a priori estimate; existence; non-existence; uniqueness; classification; method of moving planes; sliding method; etc.
(This special issue belongs to the Section General Mathematics, Analysis)
Fractional Differential Equations: Computation and Modelling with Applications submission deadline 20 Feb 2025 | 9 articles | Viewed by 11769 | Submission Open
Keywords: fractional derivatives and integrals; fractional operators; fractal-fractional derivatives and integrals; mathematical modelling; computational efficient methods; uncertainty and artificial intelligence; nonsingular kernels
(This special issue belongs to the Section General Mathematics, Analysis)
Applications of Fractional-Order Calculus in Robotics, 2nd Edition submission deadline 20 Feb 2025 | Viewed by 190 | Submission Open
Keywords: fractional calculus; fractional control; fractional modeling; robotics; fractal manipulators
Advances in Fractional Order Systems and Robust Control, 2nd Edition
edited by
submission deadline 21 Feb 2025 | 4 articles | Viewed by 3042 | Submission Open
Keywords: fractional order systems; fractional differential equations; robust control; fractional controllers; stability analysis; modeling
(This special issue belongs to the Section Engineering)
Numerical Solution and Applications of Fractional Differential Equations, 2nd Edition
edited by , and
submission deadline 25 Feb 2025 | 7 articles | Viewed by 6407 | Submission Open
Keywords: numerical methods; mathematical modeling; fractional calculus; fractional differential equations; numerical analysis; fast algorithm
(This special issue belongs to the Section Numerical and Computational Methods)
Recent Advances in Fractional Fourier Transforms and Applications, 2nd Edition submission deadline 25 Feb 2025 | 2 articles | Viewed by 1209 | Submission Open
Keywords: fractional Fourier transform; linear canonical transform; digital signal processing; fractional integral operator; partial differential equations
(This special issue belongs to the Section General Mathematics, Analysis)
Mathematical and Physical Analysis of Fractional Dynamical Systems
edited by Dimplekumar Chalishajar and Kasinathan Ravikumar
submission deadline 28 Feb 2025 | 10 articles | Viewed by 11239 | Submission Open
Keywords: functional differential and integral systems with applications; fractional PDE with applications; fractional numerical analysis and numerical simulations; oscillation/nonoscillation; feedback control and various stability analysis; boundary value problems; Markov chain process; jump processes; coupled dynamics; fractional processes; space-time fractional equations; fractional Brownian motion and Rosenblatt process; long-range dependence; time– space fractional vibration equation; convergence; eigenvalue; green function
(This special issue belongs to the Section Engineering)
Women’s Special Issue Series: Fractal and Fractional, 2nd Edition submission deadline 28 Feb 2025 | 3 articles | Viewed by 3451 | Submission Open
Keywords: fractals and fractional calculus; fractals and fractional calculus in computing; fractals and fractional calculus in mathematical physics; fractals and fractional calculus in biology and neurocomputing; fractals and fractional calculus in engineering; fractals and fractional calculus in economics; fratals and fractional calculus in educational technologies; fractional calculus and control; fractional calculus and optimization; fractional calculus and stability; fractional models and uncertainty; related fractional modeling
(This special issue belongs to the Section Complexity)
Fractal and Multifractal Analysis in Econometric Models and Empirical Finance
edited by
submission deadline 28 Feb 2025 | 2 articles | Viewed by 2508 | Submission Open
Keywords: multifractal analysis; hurst exponent; multiscale analysis; financial market efficiency; empirical finance
(This special issue belongs to the Section Mathematical Physics)
Fractals in Biophysics and Their Applications
edited by Anirban Bandyopadhyay
submission deadline 28 Feb 2025 | 3 articles | Viewed by 2248 | Submission Open
Keywords: quantum mechanics; quantum biology; biophysics; biophotonics; bioelectronics; neuroscience; brain dynamics; fractal analysis in medicine; water network in biology
(This special issue belongs to the Section Life Science, Biophysics)
Advanced Research in Fractal Properties of Nanoparticle and Its Application
edited by and Aleksandar P. Stajčić
submission deadline 28 Feb 2025 | 1 articles | Viewed by 1073 | Submission Open
Keywords: fractal dimension; surface– property relation; nanoparticles and composites; surface– synthesis/dispersion relation; grain boundary
(This special issue belongs to the Section Mathematical Physics)
Mathematical Description of Human Nervous System Using Fractals, Fractional and Integer Order Calculus
edited by
submission deadline 28 Feb 2025 | Viewed by 175 | Submission Open
Keywords: human nervous system; mathematical description using fractals; mathematical description using integer order and fractional order calculus
(This special issue belongs to the Section Life Science, Biophysics)
Applications of Fractional-Order Grey Models
edited by Shuli Yan and
submission deadline 14 Mar 2025 | 8 articles | Viewed by 8377 | Submission Open
Keywords: fractional-order; grey model; prediction; algorithm; application
(This special issue belongs to the Section Engineering)
Advances in Fractional-Order Control with Special Focus to Power Systems
edited by
submission deadline 14 Mar 2025 | Viewed by 163 | Submission Open
Keywords: fractional-order controllers; fractional-order PID controllers; fractional-order systems; adaptive fractional-order control; robust control; advanced process control; power systems; control performance assessment; system identification
(This special issue belongs to the Section Engineering)
Advances in Fractional-Order Multiagent Systems: Theory and Applications
edited by Ping Gong
submission deadline 15 Mar 2025 | 7 articles | Viewed by 9530 | Submission Open
Keywords: fractional-order dynamics; multiagent systems; distributed coordination control; nonlinear control; stability analysis; algorithm design
(This special issue belongs to the Section Engineering)
Applications of Fractional-Order Systems to Automatic Control submission deadline 15 Mar 2025 | 6 articles | Viewed by 8757 | Submission Open
Keywords: unmanned vehicles; renewable energy; electric power; manufacturing; robotics; automotive control systems; time-delay systems; modeling and control of complex systems
(This special issue belongs to the Section Engineering)
Fractional Porous Medium Type and Related Equations
edited by Petra Wittbold
submission deadline 15 Mar 2025 | Viewed by 79 | Submission Open
Keywords: time-fractional porous medium and related equations; subdiffusion processes; memory effects; stochastic perturbation; numerical approximation
(This special issue belongs to the Section General Mathematics, Analysis)
Advances in Fractional Order Derivatives and Their Applications, 3rd Edition
edited by
submission deadline 20 Mar 2025 | Viewed by 119 | Submission Open
Keywords: fractional order derivatives; fractional calculus; Caputo derivatives; Riemann– Liouville derivatives; numerical analysis; modeling; application
(This special issue belongs to the Section Numerical and Computational Methods)
Advances in Nonlinear Functional Analysis on Fractional Differential Equations, 2nd Edition
edited by
submission deadline 20 Mar 2025 | Viewed by 95 | Submission Open
Keywords: nonlinear functional analysis; control theory and applications; nonlinear fractional dynamic equations on timescale; fixed point theory; ecological systems; nonlinear dynamical systems; fractional calculus; solvability of infinite systems; sequence spaces and function spaces; nonlinear functionals and variational methods; nonlinear operators
(This special issue belongs to the Section General Mathematics, Analysis)
Fracture Analysis of Materials Based on Fractal Nature
edited by , Leandro Ferreira Friedrich and
submission deadline 25 Mar 2025 | 1 articles | Viewed by 1234 | Submission Open
Keywords: size effect; fracture; damage; experimental analysis; acoustic emission; numerical simulations
(This special issue belongs to the Section Engineering)
Fractal Analysis and Fractal Dimension in Materials Chemistry, 2nd Edition submission deadline 25 Mar 2025 | Viewed by 125 | Submission Open
Keywords: fractal dimension; fractal adsorption isotherms; catalysis; diffusion-limited reactions; fractions
Fractional-Order in Modeling and Control of Power Electronic-Based Systems submission deadline 25 Mar 2025 | Viewed by 50 | Submission Open
Keywords: power converter; digital control; model-based control; data-based control; data-driven control; modelling; fractional order
(This special issue belongs to the Section Engineering)
Fractional- and Integer-Order System: Control Theory and Applications, 2nd Edition
edited by , , , Bijnan Bandyopadhyay and
submission deadline 31 Mar 2025 | 3 articles | Viewed by 2983 | Submission Open
(This special issue belongs to the Section Engineering)
Biocomplexity and Fractal Analysis: Theory and Applications submission deadline 31 Mar 2025 | 1 articles | Viewed by 1323 | Submission Open
Keywords: biocomplexity; fractal analysis; biomathematical modeling; computer-aided diagnosis; biomarker; computational tools; biomedical imaging
(This special issue belongs to the Section Complexity)
Analysis and Applications of Fractional Calculus and Mathematical Modelling submission deadline 31 Mar 2025 | 1 articles | Viewed by 920 | Submission Open
Keywords: fractional calculus; fractional differential and integral equations; fractional models; mathematical modelling; fractional dynamics; modeling simulation; process control; application of fractional calculus; focusing on modeling and optimization.
(This special issue belongs to the Section General Mathematics, Analysis)
New Advances and Applications of Fractional Oscillate System
edited by Liang Wang
submission deadline 31 Mar 2025 | Viewed by 379 | Submission Open
Keywords: fractional calculus; fractional-order oscillate systems; stochastic dynamical systems; vibro-impact system; stochastic bifurcation and chaos
(This special issue belongs to the Section Engineering)
Fractal Analysis in Biology and Medicine
edited by
submission deadline 1 Apr 2025 | Viewed by 392 | Submission Open
Keywords: fractal analysis; fractal dimension; complexity; self-similarity; neuroscience; morphometry; cell and tissue analysis
Fractional-Order Dynamics and Control in Green Energy Systems
edited by Manashita Borah and
submission deadline 18 Apr 2025 | 3 articles | Viewed by 2266 | Submission Open
Keywords: fractional-order chaos; energy storage systems; dynamics; control systems; energy storage systems; biological systems; renewable energy applications; energy-efficient robots; green transportation
(This special issue belongs to the Section Engineering)
Advances in Boundary Value Problems for Fractional Differential Equations, 3rd Edition
edited by
submission deadline 20 Apr 2025 | 1 articles | Viewed by 275 | Submission Open
Keywords: fractional differential equations; fractional differential inclusions; fractional differential inequalities; initial value problems; boundary value problems; existence and nonexistence; uniqueness and multiplicity; stability; numerical computations
(This special issue belongs to the Section General Mathematics, Analysis)
Fractional-Order Controllers in Electronics and Automation Engineering
edited by and Didier López-Mancilla
submission deadline 30 Apr 2025 | 3 articles | Viewed by 4180 | Submission Open
Keywords: fractional-order calculus; fractional-order control; fractional-order approximations; fractional-order implementation tuning of; fractional-order controllers
(This special issue belongs to the Section Engineering)
Enhancing Pain Assessment and Anesthesia Management: Fractional Modeling with AI
edited by
submission deadline 30 Apr 2025 | 1 articles | Viewed by 435 | Submission Open
Keywords: anesthesia and fractional calculus and AI; pain and fractional calculus and AI; neuro monitoring; fractional calculus
(This special issue belongs to the Section Life Science, Biophysics)
Fractal Analysis and Its Applications in Materials Science submission deadline 30 Apr 2025 | Viewed by 193 | Submission Open
Keywords: fractal analysis; fractal materials; fractals media; metamaterial characterization; acoustic characterization; porous materials; micropolar materials; poroelastic /elastic materials; solid and fluid mechanics; self-similar media; fractal analysis and applications in materials science
(This special issue belongs to the Section Engineering)
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