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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. The journal’s Editor-in-Chief and/or designated EBM 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. For any inquiries related to a Special Issue, please contact the Editorial Office.

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Fractal Mechanics of Engineering Materials

edited by

Mohd Nasir Tamin

and

Seyed R. Koloor

submission deadline 30 Apr 2024 | 7 articles | Viewed by 10967 | Submission Open

(This special issue belongs to the Section Engineering)

Fractional-Order Chaotic System: Control and Synchronization, 2nd Edition

edited by

Song Zheng

Emad E. Mahmoud

and

Yangquan Chen

submission deadline 30 Apr 2024 | 5 articles | Viewed by 5046 | Submission Open

Keywords: fractional-order; complex systems; chaos; synchronization; control; stabilization; consensus; identification; modelling

(This special issue belongs to the Section Complexity)

Fractional Differential Operators with Classical and New Memory Kernels

edited by

Dimiter Prodanov

and

Jordan Hristov

submission deadline 30 Apr 2024 | 4 articles | Viewed by 4641 | Submission Open

Keywords: fractional operators; memory kernels; biomechanical and medical models; 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 non-local 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)

Advances in Fractional Order Derivatives and Their Applications, 2nd Edition

edited by

Sameerah Jamal

submission deadline 30 Apr 2024 | 5 articles | Viewed by 3498 | 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)

Modern Methods for Fractal and Multifractal Analysis of Time Series: Theoretical Frameworks and Practical Applications

edited by

Lyudmyla Kirichenko

submission deadline 30 Apr 2024 | 2 articles | Viewed by 2231 | Submission Open

Keywords: fractal/multifractal analysis; self-similarity; time series; long-term memory; scaling properties; artificial intelligence; applications

(This special issue belongs to the Section Complexity)

Fractional Order Systems with Time Delay: Theory, Stability Analysis and Applications

edited by Xujun Yang and Xiaofeng Chen

submission deadline 30 Apr 2024 | 2 articles | Viewed by 1968 | Submission Open

Keywords: fractional-order systems; distributed-order systems; fractional-order neural networks; delay; impulse; and perturbance; bifurcation; chaos; and synchronization; stability analysis; controller design

(This special issue belongs to the Section Complexity)

Fractional-Order Circuits, Systems, and Signal Processing, 2nd Edition

edited by

Norbert Herencsar

Shibendu Mahata

Esteban Tlelo-Cuautle

and

Ivo Petráš

submission deadline 30 Apr 2024 | 1 articles | Viewed by 1461 | 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)

Fractional-Order Dynamics and Control in Green Energy Systems

edited by Manashita Borah and

Christos Volos

submission deadline 30 Apr 2024 | Viewed by 301 | 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)

New Trends on Generalized Fractional Calculus

edited by

Milton Ferreira

Maria Manuela Fernandes Rodrigues

and

Nelson Felipe Loureiro Vieira

submission deadline 15 May 2024 | 8 articles | Viewed by 9218 | 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)

Application of Anomalous Diffusion Modeling Based on Fractal and Fractional Derivatives

edited by

Minghua Chen

, Jianxiong Cao,

An Chen

and

Hossein Jafari

submission deadline 15 May 2024 | 3 articles | Viewed by 3009 | 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)

Observability and Observer Design of Fractional-Order Nonlinear Systems

edited by

Guillermo Fernández-Anaya

Oscar Martínez-Fuentes

and

Aldo Jonathan Muñoz-Vazquez

submission deadline 15 May 2024 | 1 articles | Viewed by 1555 | Submission Open

Keywords: nonlinear observers; fractional differential equations; generalized calculus; observer theory; fault detection; synchronization; observer-based controllers

(This special issue belongs to the Section Mathematical Physics)

q-Fractional Calculus/Differential Equations and Related Applications

edited by

Jung Yoog Kang

and

Cheon-Seoung Ryoo

submission deadline 15 May 2024 | Viewed by 177 | Submission Open

Keywords: foundations of fractional analysis; fractional-order derivatives and integrals; fractional transforms; special functions; quantum calculus; linear and nonlinear fractional analysis; q-fractional differential equations; fractional differential equations; fractional partial differential equations; fractional continuous models; dynamical systems based on fractional calculus; fractional analysis applications; numerical analysis

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

Advances in Boundary Value Problems for Fractional Differential Equations, 2nd Edition

edited by

Rodica Luca

submission deadline 21 May 2024 | 9 articles | Viewed by 8521 | Submission Open

Keywords: fractional differential equations; fractional differential inclusions; fractional differential inequalities; initial value problems; boundary value problems; existence; nonexistence; uniqueness; multiplicity; stability; numerical computations

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

Advances in Fractional Order Systems and Robust Control, 2nd Edition

edited by

Feng Liu

submission deadline 21 May 2024 | Viewed by 81 | Submission Open

Keywords: fractional order systems; fractional differential equations; robust control; fractional controllers; stability analysis; modeling

(This special issue belongs to the Section Engineering)

Analysis of Heat Conduction and Anomalous Diffusion in Fractional Calculus

edited by

Aloisi Somer

and

Ervin K. Lenzi

submission deadline 30 May 2024 | Viewed by 177 | 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)

Fractional Gravity/Cosmology in Classical and Quantum Regimes

edited by

Seyed Meraj Mousavi Rasouli

and

Shahram Jalalzadeh

submission deadline 31 May 2024 | 4 articles | Viewed by 6337 | Submission Open

Keywords: fractional calculus; fractional derivatives; Riesz fractional operator; Caputo fractional operator; fractional Brownian motion; Lé vy 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)

Fractal and Fractional Analysis in Biomedical Sciences and Engineering

edited by

Andjelija Ž. Ilić

submission deadline 31 May 2024 | 5 articles | Viewed by 5793 | Submission Open

Keywords: fractal and multifractal analysis; fractal lacunarity analysis; fractional calculus; fractional differential equations; convergence and stability analysis; biological system complexity; non-linear biosystem dynamics; medical image and data analysis; neural networks and graphs; long-term correlation tracking

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

Recent Advances in Fractional Differential Equations and Their Applications, 2nd Edition

edited by

Xiaoli Chen

Dongfang Li

and Ting Gao

submission deadline 31 May 2024 | 4 articles | Viewed by 3971 | Submission Open

Keywords: nonlocal differential equation; fractional differential equation; stochastic differential equation; numerical method; machine learning methods

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

Optimal Control Problems for Fractional Differential Equations

edited by

Gisèle M. Mophou

submission deadline 31 May 2024 | 3 articles | Viewed by 3934 | Submission Open

Keywords: fractional differential equations; optimal control; fractional differential inequalities; time fractional and space fractional derivatives; generalized fractional derivatives; optimal control on bounded and unbounded domain; optimal control on network; Rieman-Liouville fractional derivative; Caputo fractional derivative; generalized fractional derivative; fractional Laplace operator; optimality systems; linear fractional differential equations; nonlinear fractional differential equations

(This special issue belongs to the Section Engineering)

Fractional Evolutionary Equations and Modeling of Dissipative Processes, 2nd Edition

edited by

Arsen V. Pskhu

and

Roman Ivanovich Parovik

submission deadline 31 May 2024 | 3 articles | Viewed by 3334 | Submission Open

Keywords: diffusion wave equations; direct and backward problems; problems without initial conditions; mathematical modeling of microseisms; Sel’ kov fractional dynamical system; distributed order fractional diffusion; memory density; Hurst exponents; fractional Riccati equation; variable order fractional derivatives; regular and chaotic regimes; Dubovsky's fractional dynamic system.

(This special issue belongs to the Section Mathematical Physics)

Spectral Methods for Fractional Functional Models

edited by

and

submission deadline 31 May 2024 | 2 articles | Viewed by 2246 | Submission Open

Keywords: spectral methods for fractional partial differential equations; spectral methods for fractional integral equations; spectral methods for integro-differential equations involving fractional operators; spectral methods for systems of fractional differential equations

(This special issue belongs to the Section Mathematical Physics)

Inverse Problems for Fractional Differential Equations

edited by

Jorge Mario Cruz-Duarte

submission deadline 31 May 2024 | 2 articles | Viewed by 1808 | Submission Open

Keywords: inverse problems; fractional differential equations; fractional derivatives; non-integer derivatives; fractional models; chaotic systems; time-fractional diffusion; spatial-fractional diffusion; non-linear fractional differential equations; pseudo-differential equations; fractional reactions

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

Fractal and Multifractal Analysis in Econometric Models and Empirical Finance

edited by

Sun-Yong Choi

submission deadline 31 May 2024 | 1 articles | Viewed by 1331 | Submission Open

Keywords: multifractal analysis; hurst exponent; multiscale analysis; financial market efficiency; empirical finance

(This special issue belongs to the Section Mathematical Physics)

Electric Drive Control Using Fractal and Fractional Calculus

edited by

Marcel Nicola

Dan Selisteanu

and Cosmin Ionete

submission deadline 31 May 2024 | Viewed by 233 | Submission Open

Keywords: fractional-order system; fractals; electric drive control; energy storage system; power electronic converters; stability analysis; fractional calculus

(This special issue belongs to the Section Engineering)

New Insights and Trends in Fractional-Order Dynamical Networks, Their Control and Synchronization

edited by

Gualberto Solís-Perales

submission deadline 31 May 2024 | Viewed by 102 | Submission Open

Keywords: fractional networks; control of fractional systems and networks; synchronization of fractional networks and systems; dynamic evolution of connections in fractional networks

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

Recent Advances in Adaptive Fractional Sliding Mode Control

edited by Mehran Rahmani

submission deadline 1 Jun 2024 | 1 articles | Viewed by 1421 | Submission Open

Keywords: sliding mode control; fractional calculus; robustness; chattering phenomena

(This special issue belongs to the Section Engineering)

Applications of Fractal Analysis in Underground Engineering

edited by

Shihao Tu

, Lei Zhang,

Chen Wang

Cun Zhang

, Defu Zhu and Kaijun Miao

submission deadline 12 Jun 2024 | 4 articles | Viewed by 5435 | Submission Open

(This special issue belongs to the Section Engineering)

Advanced Modeling and Methods of Statistical Processing of Stochastic Signals in Fractional Dynamic Systems

edited by

Serhii Lupenko

and Jacek Leśkow

submission deadline 14 Jun 2024 | 3 articles | Viewed by 3106 | 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)

Applications of Fractional-Order Calculus in Robotics

edited by

Abhaya Pal Singh

and

Kishore Bingi

submission deadline 15 Jun 2024 | 9 articles | Viewed by 14089 | Submission Open

Keywords: fractional calculus; fractional control; fractional modeling; robotics; manipulators fractal

(This special issue belongs to the Section Engineering)

Anomalous Diffusion and Relaxations in Liquid Crystals: Fractal and Fractional Behavior

edited by Rafael Soares Zola and

Ervin K. Lenzi

submission deadline 15 Jun 2024 | Viewed by 373 | 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)

Fractal Theory and Models in Nonlinear Dynamics and Their Applications

edited by

Luis Manuel Palacios-Pineda

and

Oscar Martínez-Romero

submission deadline 20 Jun 2024 | 6 articles | Viewed by 5139 | Submission Open

(This special issue belongs to the Section Mathematical Physics)

Stochastic and Fractional Differential Equations: Attractor, Invariant Measure and Their Relationship

edited by Dingshi Li and Chunmei Zhang

submission deadline 20 Jun 2024 | 2 articles | Viewed by 2171 | Submission Open

Keywords: random dynamical system; stochastic differential equation; fractional differential equation; random attractor; invariant measures; random fractional

(This special issue belongs to the Section Mathematical Physics)

Feature Papers for Numerical and Computational Methods Section

edited by

Riccardo Caponetto

submission deadline 25 Jun 2024 | 12 articles | Viewed by 12990 | 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)

Fractional Equations and Calculation Methods in Exploration Seismology

edited by

Jidong Yang

and Zeyu Zhao

submission deadline 27 Jun 2024 | 3 articles | Viewed by 3370 | Submission Open

Keywords: fractional wave equation; fractional Laplacian; calculation of fractional equation; seismic modeling; imaging and inversion

(This special issue belongs to the Section Mathematical Physics)

Advances in Fractional Integral and Derivative Operators with Applications

edited by

Rekha Srivastava

submission deadline 30 Jun 2024 | 15 articles | Viewed by 15393 | Submission Open

Keywords: theoretical advances involving operators of fractional integrals and fractional derivatives; applications involving chaos and dynamical systems based upon fractional calculus; applications based upon fractional-order ordinary and partial differential equations; fractional-order differ-integral and integro-differential equations; fractional-order integrals and derivatives associated with higher transcendental functions including special functions of mathematical physics and applied mathematics; inequalities and identities involving integrals and derivatives of a fractional order

(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

edited by

Jinxi Zhang

Xuefeng Zhang

, Driss Boutat and

Dayan Liu

submission deadline 30 Jun 2024 | 7 articles | Viewed by 6944 | Submission Open

Keywords: image processing; image fusion; image denoising; image enhancement; analysis and control of fractional systems; singular fractional systems; intelligent fractional control; high-performance control; non-asymptotic fractional state estimation; fractional numerical solution and simulation

(This special issue belongs to the Section Engineering)

Fractional Integral Inequalities and Applications, 2nd Edition

edited by

Artion Kashuri

and

Hari Mohan Srivastava

submission deadline 30 Jun 2024 | 6 articles | Viewed by 6563 | Submission Open

Keywords: fractional integral inequalities; generalized convexity; numerical estimations; quantum calculus; multivariate analysis; means; operator theory; approximation theory

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

Advance on the Fractal and Fractional Calculus in Electrical and Electronic Engineering

edited by

Kang-Jia Wang

and

Inés Tejado

submission deadline 30 Jun 2024 | 4 articles | Viewed by 4035 | Submission Open

(This special issue belongs to the Section Engineering)

Fractional Models and Statistical Applications

edited by

Yuliya Mishura

, Kostiantyn Ralchenko and Anton Yurchenko-Tytarenko

submission deadline 30 Jun 2024 | 3 articles | Viewed by 3164 | Submission Open

(This special issue belongs to the Section Probability and Statistics)

Recent Advances in Fractional-Order Time Delay Systems

edited by

Feifei Du

and Zeyu Liu

submission deadline 30 Jun 2024 | 1 articles | Viewed by 1305 | Submission Open

Keywords: fractional-order systems; complex networks; neural networks; time delay; stability; synchronization

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

Application of Fractional Calculus as an Interdisciplinary Modeling Framework, 2nd Edition

edited by

and

submission deadline 30 Jun 2024 | 1 articles | Viewed by 1295 | Submission Open

Keywords: general fractional calculus; special functions; integral transforms; harmonic analysis; fractional variational calculus; ODEs; PDEs and integral equations and systems; wave equation; evolution equation; mathematical models of phenomena; fractional quantum fields; nonlinear control methods; fractional-order controllers; bio-medical applications; economic models with memory; numerical and approximation methods; computational procedures and algorithms

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

Numerical Solution and Applications of Fractional Differential Equations, 2nd Edition

edited by

Libo Feng

Yang Liu

and

Lin Liu

submission deadline 30 Jun 2024 | 1 articles | Viewed by 1116 | 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)

Fractal and Multifractal Analysis in Environmental, Medical and Technical Fields: Pattern Recognition, Analysis and Processing of Images

edited by

Erveton Pinheiro Pinto

Marcelo Pires

and

Nilson dos Santos Ferreira

submission deadline 30 Jun 2024 | Viewed by 356 | 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)

Fractional Differential Equations: Computation and Modelling with Applications

edited by

Rajarama Mohan Jena

and

Snehashish Chakraverty

submission deadline 15 Jul 2024 | 8 articles | Viewed by 8093 | 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)

Fractional Calculus and Nonlinear Analysis: Theory and Applications

edited by

Wei-Shih Du

Marko Kostić

and

Daniel Velinov

submission deadline 15 Jul 2024 | 3 articles | Viewed by 3795 | 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)

Women’s Special Issue Series: Fractal and Fractional, 2nd Edition

edited by

Ivanka Stamova

Carla M. A. Pinto

and

Dana Copot

submission deadline 15 Jul 2024 | 1 articles | Viewed by 1057 | 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)

New Insights into Random Walks and Diffusion Equations

edited by Marco Antonio Alves Da Silva, José Carlos Cressoni and

Gandhimohan M. Viswanathan

submission deadline 18 Jul 2024 | Viewed by 100 | 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)

Numerical and Exact Methods for Nonlinear Differential Equations and Applications in Physics

edited by

Yusuf Gürefe

submission deadline 25 Jul 2024 | 11 articles | Viewed by 12935 | 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)

Caputo Fractional Difference Equations and Its Applications

edited by

Churong Chen

and

Dorota Mozyrska

submission deadline 30 Jul 2024 | Viewed by 234 | Submission Open

Keywords: caputo fractional difference equations; mathematical modeling; stability analysis; numerical methods

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

Recent Advances in Fractional-Order Neural Networks: Theory and Application

edited by

Zhouchao Wei