Fractal and Fractional

Fractional Calculus, Quantum Calculus and Special Functions in Complex Analysis

edited by

and

submission deadline 31 Mar 2026 | 8 articles | Viewed by 10770 | Submission Open

Keywords: univalent functions; special functions; fractional operator; q– operator; differential subordination; differential superordination; quantum calculus

(This special issue belongs to the Section General Mathematics, Analysis)

Analysis and Applications of Fractional Calculus and Mathematical Modelling

edited by

Marcelo Kaminski Lenzi

submission deadline 31 Mar 2026 | 6 articles | Viewed by 7777 | 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)

Fractional Order Modelling of Dynamical Systems

edited by

Zubair Ahmad

submission deadline 31 Mar 2026 | 4 articles | Viewed by 5204 | Submission Open

Keywords: fractional derivatives; numerical methods of fractional order systems; fractional dynamical systems; stability analysis; fractional models in fluid dynamics; disease dynamics and epidemiology; fractional modelling with applications

(This special issue belongs to the Section Engineering)

Fractional Derivatives in Mathematical Modeling and Applications

edited by

Damian Słota

,

Rafal Brociek

and

Edyta Hetmaniok

submission deadline 31 Mar 2026 | 2 articles | Viewed by 2181 | Submission Open

Keywords: fractional calculus; mathematical modeling; fractional differential equation; numerical methods; fractional integro-differential equations; optimization problems

(This special issue belongs to the Section Numerical and Computational Methods)

Fractal Dimensions and Their Implications in Characterization of Porous Media

edited by

Boming Yu

, Boqi Xiao and

Dahua Shou

submission deadline 31 Mar 2026 | 1 articles | Viewed by 826 | Submission Open

Keywords: fractal; porous media; thermal conductivity; permeability; electrical conductivity; diffusivity; pore-fracture media

(This special issue belongs to the Section Engineering)

Fractal and Multifractal Analysis in Geophysics and Petrophysics: Theory, Methods, and Applications

edited by

Peiqiang Zhao

, Lingyun Kong and

Mehdi Ostadhassan

submission deadline 31 Mar 2026 | Viewed by 671 | Submission Open

Keywords: porous media; fractal and multifractal; petrophysics; geophysics; rock mechanics; unconventional resources

(This special issue belongs to the Section Engineering)

Metric Spaces with Its Application to Fractional Differential Equations, Second Edition

edited by Monica-Felicia Bota,

Liliana Guran

and

Khurram Shabbir

submission deadline 31 Mar 2026 | Viewed by 641 | 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)

Advances in Fractional-Order Control for Nonlinear Systems

edited by

Masoud Sotoodeh-Bahraini

and

Pedro Ferreira

submission deadline 31 Mar 2026 | 1 articles | Viewed by 465 | Submission Open

Keywords: fractional-order control; nonlinear systems; fractional calculus; variable-order controllers; adaptive control; robust control; stability analysis; Lyapunov methods; fractional PID controllers; backstepping control; memory-dependent systems; hybrid fractional– integer control; computational complexity in control; real-time control systems; human– robot interaction; power electronics control; biomedical systems control; mechatronic systems; industrial automation; process control

(This special issue belongs to the Section Engineering)

Fractional Calculus in Signal, Imaging Processing and Machine Learning, 2nd Edition

edited by

Yi-Fei Pu

submission deadline 31 Mar 2026 | Viewed by 396 | Submission Open

Keywords: fractional-order signal processing; fractional-order image processing; fractional-order machine learning; fractional-order computing law; fractional-order neuromorphic computing

(This special issue belongs to the Section Optimization, Big Data, and AI/ML)

Fractals in Physiology and Medicine

edited by

Igor V. Pantic

submission deadline 31 Mar 2026 | Viewed by 272 | Submission Open

Keywords: fractal analysis; physiological signals; biomedical imaging; machine learning in physiology; complex systems; computational physiology

(This special issue belongs to the Section Life Science, Biophysics)

Advances in Fractional Order Signal Processing: Theory and Methods

edited by Yuan-Min Li and Deyun Wei

submission deadline 31 Mar 2026 | Viewed by 174 | Submission Open

Keywords: fractional integral transform; sparse fractional order transform; sparse representation and fast algorithm; graph transform; sampling and filtering; convolutional neural network; digital signal processing

(This special issue belongs to the Section Engineering)

Fractional-Order Modeling in Data-Driven Intelligent Systems: From Optimization to AI/ML Applications

edited by Yan Li and Ziquan Yu

submission deadline 15 Apr 2026 | Viewed by 141 | Submission Open

Keywords: fractional-order calculus in AI/ML; control theoretic ML; large-scale optimization; safe/explainable AI; real-time ML; interdisciplinary integration

(This special issue belongs to the Section Optimization, Big Data, and AI/ML)

Nonlinear Fractional Maps: Dynamics and Control

edited by Telksnys Tadas

submission deadline 20 Apr 2026 | 1 articles | Viewed by 1451 | Submission Open

(This special issue belongs to the Section General Mathematics, Analysis)

Advanced Numerical Methods for Fractional Functional Models

edited by

Kamyar Hosseini

,

Khadijeh Sadri

,

Evren Hınçal

,

Soheil Salahshour

and Farzaneh Alizadeh

submission deadline 30 Apr 2026 | 4 articles | Viewed by 6768 | Submission Open

Keywords: numerical methods; approximation methods; fractional differential equations; fractional partial differential equations; fractional integral equations; fractional functional models

(This special issue belongs to the Section Numerical and Computational Methods)

Mathematical and Physical Analysis of Fractional Dynamical Systems, Second Edition

edited by Dimplekumar N. Chalishajar and Kasinathan Ravikumar

submission deadline 30 Apr 2026 | 6 articles | Viewed by 4915 | 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)

Fractal Analysis and Its Applications in Materials Science

edited by

Zine El Abiddine Fellah

submission deadline 30 Apr 2026 | 3 articles | Viewed by 4239 | 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)

Fractional-Order Modeling and Control for Complex Dynamic Systems: Methodologies and Applications

edited by Necdet Sinan Özbek,

Ying Luo

and

Yangquan Chen

submission deadline 30 Apr 2026 | 3 articles | Viewed by 1828 | Submission Open

Keywords: fractional-order systems; fractional calculus; complex dynamic systems; fractional-order control; non-integer order modeling; robust control; adaptive control; sliding mode control; stability analysis; system identification; memory and hereditary systems; numerical methods for fractional systems; networked and distributed systems; machine learning in fractional control; biomedical applications of fractional models; energy systems modeling; optimization in fractional-order systems; time-domain and frequency-domain analysis

(This special issue belongs to the Section Engineering)

Advances in Fractal and Multifractal Analysis Driven by Machine Learning Approaches

edited by Lyudmyla Kirichenko

submission deadline 30 Apr 2026 | 1 articles | Viewed by 1317 | Submission Open

Keywords: fractal/multifractal analysis; self-similarity; time series; long-term memory; scaling properties; artificial intelligence; machine learning; deep learning; complexity analysis; anomaly detection; feature extraction; applications

(This special issue belongs to the Section Optimization, Big Data, and AI/ML)

Artificial Intelligence and Fractional Modelling for Energy Systems

edited by

Alejandro Ramos Martín

and

Federico León Zerpa

submission deadline 30 Apr 2026 | 1 articles | Viewed by 942 | Submission Open

Keywords: adaptive and learning algorithms; digital twin behaviour-matching algorithms; fractional-order modelling; optimisation methods; edge artificial intelligence; AI at the Edge; AI on the Edge; edge computing with AI; peripheral AI; peripheral artificial intelligence; decentralised AI computing; real-time AI; low-latency AI processing; real-time AI inference; AI in embedded systems; edge machine learning (Edge ML); AI for smart sensors

(This special issue belongs to the Section Optimization, Big Data, and AI/ML)

Fractional Order Mechatronics

edited by

Ying Luo

and Pengchong Chen

submission deadline 30 Apr 2026 | Viewed by 611 | 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)

Fractional Differential Equations: Computation and Modelling with Applications, 2nd Edition

edited by Rajarama Mohan Jena and

Snehashish Chakraverty

submission deadline 30 Apr 2026 | Viewed by 389 | Submission Open

Keywords: fractional derivatives and integrals; fractional operators; fractal– fractional derivatives and integrals; mathematical modelling; computational efficient methods; uncertainty and artificial intelligence; non-singular kernels

New Perspectives and Applications of Fractional Order Modeling in Energy Systems

edited by

Marco Antonio Polo-Labarrios

submission deadline 30 Apr 2026 | Viewed by 178 | Submission Open

Keywords: fractional order differential equations; fractional modeling; fractional dynamics; anomalous transport; thermal memory effects; multiscale energy systems; fractional simulation; numerical algorithms in fractional calculus

(This special issue belongs to the Section Engineering)

Advances in Fractal Analysis for Biomedical Image: Methods and Applications

edited by Paraschiva A. Postolache and

Maricel Agop

submission deadline 30 Apr 2026 | Viewed by 125 | Submission Open

Keywords: fractal analysis; biomedical imaging; fractal dimension; image processing

(This special issue belongs to the Section Life Science, Biophysics)

Fractal Dimension Analysis in Brain Function: From Basic Mechanisms to Clinical Frontiers

edited by

Camillo Porcaro

submission deadline 1 May 2026 | Viewed by 263 | Submission Open

Keywords: innovative methods for FD extraction and analysis in neural signals; FD-driven improvements in BCI design and decoding strategies; personalised neuromodulation by tailoring NIBS interventions using FD metrics; FD as a non-invasive biomarker for early diagnosis and monitoring of neurological and psychiatric disorders; multimodal and cross-modal applications combining FD with EEG; MEG; fMRI; and TMS; new theoretical frameworks linking brain criticality; fractal geometry; and functional connectivity

(This special issue belongs to the Section Life Science, Biophysics)

Distributed Control and Optimization of Fractional-Order Systems: Theory and Applications

edited by Jun Shen and Cuihong Wang

submission deadline 16 May 2026 | 2 articles | Viewed by 2261 | 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)

Fractional Dynamics and Control in Multi-Agent Systems and Networks

edited by Huaiqin Wu and

Cheng Hu

submission deadline 20 May 2026 | 2 articles | Viewed by 1702 | Submission Open

Keywords: system model; fractional-order dynamics; MASs and CNs; stability analysis; nonlinear control

(This special issue belongs to the Section Engineering)

Fractal Dynamics of Complex Systems in Society and Behavioral Science

edited by

Trung V. Phan

and Mingshu Peng

submission deadline 20 May 2026 | 1 articles | Viewed by 1437 | Submission Open

Keywords: fractal dynamics; scale free; collective behavior; self-organization; adaptive and intelligent systems

(This special issue belongs to the Section Life Science, Biophysics)

Data-Driven Modeling, Prediction and Control of Fractional-Order Systems

edited by Fudong Ge,

Ying Luo

and

Yangquan Chen

submission deadline 30 May 2026 | 3 articles | Viewed by 2785 | 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

Xiao-Jun Yang

, Wenxue Zhou, Sunil Dutt Purohit,

Ali Turab

and Ahmed Refaie Ali

submission deadline 31 May 2026 | 17 articles | Viewed by 18783 | 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

Pier Luigi Gentili

submission deadline 31 May 2026 | 7 articles | Viewed by 18211 | Submission Open

Keywords: complex systems; pattern recognition; image processing; fractal descriptors; neural networks; network science

Advances in Fractional Operators: Mathematical Perspectives and Multidisciplinary Applications

edited by Leandro Tavares and

J. Vanterler Da C. Sousa

submission deadline 31 May 2026 | 5 articles | Viewed by 4249 | 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

Bipan Hazarika

submission deadline 31 May 2026 | 3 articles | Viewed by 3335 | 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

edited by

Dianshi Xiao

,

Xixin Wang

and

Nengwu Zhou

submission deadline 31 May 2026 | 3 articles | Viewed by 1811 | 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

edited by

Ljubiša D. R. Kočinac

and

Tayyab Kamran

submission deadline 31 May 2026 | 1 articles | Viewed by 1153 | 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

Kambiz Razminia

submission deadline 31 May 2026 | Viewed by 97 | Submission Open

Keywords: fractal distributions; fractal parameters; petrophysical properties; fluid flow in fractal porous media; fractal partial differential equations; fractional differential equations

(This special issue belongs to the Section Engineering)

Numerical Analysis and Iterative Methods for Fractional Differential Equations

edited by

Mudassir Shams

and

Bruno Carpentieri

submission deadline 13 Jun 2026 | 3 articles | Viewed by 2184 | 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

Zine El Abiddine Fellah

, Jizhen Zhang and

Quanzhong Guan

submission deadline 15 Jun 2026 | 6 articles | Viewed by 4681 | 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

Zeeshan Ali

and

Sandra Pinelas

submission deadline 16 Jun 2026 | 1 articles | Viewed by 1036 | 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

Jin-Xi Zhang

,

Xuefeng Zhang

, Driss Boutat and

Da-Yan Liu

submission deadline 25 Jun 2026 | 8 articles | Viewed by 8771 | 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

Yusuf Gürefe

submission deadline 30 Jun 2026 | 10 articles | Viewed by 9557 | 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)

Fractional Gravity/Cosmology in Classical and Quantum Regimes, Second Edition

edited by

Seyed Meraj Mousavi Rasouli

and

Shahram Jalalzadeh

submission deadline 30 Jun 2026 | 2 articles | Viewed by 5478 | 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

Feng Feng

and

Qiang Li

submission deadline 30 Jun 2026 | 2 articles | Viewed by 2634 | 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

edited by

Ernesto Zambrano-Serrano

and

Miguel A. Platas-Garza

submission deadline 30 Jun 2026 | 1 articles | Viewed by 2103 | 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)

Mathematical and Numerical Analysis of Fractional Evolution Equations and Applications

edited by

Naben Parumasur

,

Vijay Kumar Kukreja

and

Pravin Singh

submission deadline 30 Jun 2026 | 3 articles | Viewed by 1827 | 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)

Fractals in Earthquake and Atmospheric Science

edited by

Dimitrios Nikolopoulos

submission deadline 30 Jun 2026 | 3 articles | Viewed by 1684 | 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)

Applications of Fractal Analysis in Structural Geology

edited by

Jing Ba

, Yuhang Guo and

Cong Luo

submission deadline 30 Jun 2026 | 1 articles | Viewed by 1377 | 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

edited by

Dimiter Prodanov

and

Jordan Hristov

submission deadline 30 Jun 2026 | 1 articles | Viewed by 916 | 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)

New Horizons in Fractional and Fractal Dynamics: Unraveling Complexity in Chaotic Systems

edited by

Song Zheng

and

Liguo Yuan

submission deadline 30 Jun 2026 | 1 articles | Viewed by 916 | 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)

Fractional Stochastic Process: Theory and Applications

edited by

Wanqing Song

and

Francesco Villecco

submission deadline 30 Jun 2026 | 1 articles | Viewed by 883 | 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)

Advances in Fractional-Order Control and Optimization for Sustainable Energy Systems

edited by

Jiuwu Hui

and

Aldo Jonathan Muñoz-Vazquez

submission deadline 30 Jun 2026 | 1 articles | Viewed by 872 | 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)

Journal Menu

Journal Browser

Special Issues

Further Information

Guidelines

MDPI Initiatives

Follow MDPI