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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 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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Mathematical and Physical Analysis of Fractional Dynamical Systems

edited by Dimplekumar Chalishajar and Kasinathan Ravikumar

submission deadline 28 Feb 2025 | 8 articles | Viewed by 8937 | 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 and Multifractal Analysis in Econometric Models and Empirical Finance

edited by

Sun-Yong Choi

submission deadline 28 Feb 2025 | 1 articles | Viewed by 1773 | 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 | Viewed by 330 | 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)

Mathematical Description of Human Nervous System Using Fractals, Fractional and Integer Order Calculus

edited by

Stefan Balint

submission deadline 28 Feb 2025 | Viewed by 84 | 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)

Advances in Fractional-Order Control with Special Focus to Power Systems

edited by

Martin Čech

submission deadline 14 Mar 2025 | Viewed by 91 | 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 Derivatives and Their Applications, 3rd Edition

edited by

Sameerah Jamal

submission deadline 20 Mar 2025 | Viewed by 64 | 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

Bipan Hazarika

submission deadline 20 Mar 2025 | Viewed by 37 | 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 and Fractal Dimension in Materials Chemistry, 2nd Edition

edited by

Gianina Dobrescu

Florica Papa

and

Razvan State

submission deadline 25 Mar 2025 | Viewed by 26 | Submission Open

Keywords: fractal dimension; fractal adsorption isotherms; catalysis; diffusion-limited reactions; fractions

Fractional-Order in Modeling and Control of Power Electronic-Based Systems

edited by

Ton Duc Do

and

Duy Truong Duong

submission deadline 25 Mar 2025 | Viewed by 13 | 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

Thach Ngoc Dinh

Shyam Kamal

Rajesh Kumar Pandey

, Bijnan Bandyopadhyay and

Jun Huang

submission deadline 31 Mar 2025 | 2 articles | Viewed by 2390 | Submission Open

(This special issue belongs to the Section Engineering)

Biocomplexity and Fractal Analysis: Theory and Applications

edited by

Annamaria Zaia

and

Pierluigi Maponi

submission deadline 31 Mar 2025 | 1 articles | Viewed by 1094 | Submission Open

Keywords: biocomplexity; fractal analysis; biomathematical modeling; computer-aided diagnosis; biomarker; computational tools; biomedical imaging

(This special issue belongs to the Section Complexity)

New Advances and Applications of Fractional Oscillate System

edited by Liang Wang

submission deadline 31 Mar 2025 | Viewed by 332 | 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)

Analysis and Applications of Fractional Calculus and Mathematical Modelling

edited by

Marcelo Kaminski Lenzi

submission deadline 31 Mar 2025 | Viewed by 134 | 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 Dynamics and Control in Green Energy Systems

edited by Manashita Borah and

Christos Volos

submission deadline 18 Apr 2025 | Viewed by 386 | 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

Rodica Luca

submission deadline 20 Apr 2025 | Viewed by 31 | 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

Allan G. Soriano-Sánchez

and Didier López-Mancilla

submission deadline 30 Apr 2025 | 3 articles | Viewed by 3602 | 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)

Fractal Analysis and Its Applications in Materials Science

edited by

Zine El Abiddine Fellah

submission deadline 30 Apr 2025 | Viewed by 130 | 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)

Enhancing Pain Assessment and Anesthesia Management: Fractional Modeling with AI

edited by

Martine Neckebroek

submission deadline 30 Apr 2025 | Viewed by 113 | 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)

Advanced Numerical Methods for Fractional Functional Models

edited by

Kamyar Hosseini

Khadijeh Sadri

Evren Hınçal

Soheil Salahshour

and Farzaneh Alizadeh

submission deadline 30 Apr 2025 | Viewed by 64 | 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)

Applications of Fractal Analysis in Underground Engineering

edited by

Shihao Tu

, Lei Zhang,

Chen Wang

Cun Zhang

, Defu Zhu and Kaijun Miao

submission deadline 1 May 2025 | 6 articles | Viewed by 7461 | Submission Open

(This special issue belongs to the Section Engineering)

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

edited by Jun Shen and Cuihong Wang

submission deadline 16 May 2025 | Viewed by 80 | 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)

Analysis of Heat Conduction and Anomalous Diffusion in Fractional Calculus

edited by

Aloisi Somer

and

Ervin K. Lenzi

submission deadline 30 May 2025 | 1 articles | Viewed by 666 | 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)

Mathematical Inequalities in Fractional Calculus and Applications, 2nd Edition

edited by

Seth Kermausuor

and

Eze Nwaeze

submission deadline 31 May 2025 | Viewed by 77 | Submission Open

Keywords: fractional calculus; caputo derivative; riemann-liouville derivative; discrete fractional calculus; fractals; fractional differential equations; mathematical inequalities; time scales

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

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

edited by

Serhii Lupenko

and Jacek Leśkow

submission deadline 13 Jun 2025 | 3 articles | Viewed by 4076 | 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

Bruno Carpentieri

submission deadline 13 Jun 2025 | Viewed by 46 | 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)

Fractional Systems, Integrals and Derivatives: Theory and Application

edited by

Andrey Zahariev

and

Hristo Kiskinov

submission deadline 30 Jun 2025 | 3 articles | Viewed by 1931 | 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)

Multi-scale and Fractal Research on Advanced Manufacturing and Tribology

edited by

Feng Feng

and

Qiang Li

submission deadline 30 Jun 2025 | Viewed by 95 | 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)

Advanced Fractional Sliding Mode Control for Dynamic and Robotic Systems

edited by Mehran Rahmani

submission deadline 30 Jun 2025 | Viewed by 46 | Submission Open

Keywords: fractional sliding mode control; robust control; dynamic systems; robotics

(This special issue belongs to the Section Engineering)

Recent Advances in Fractional-Order Equations and Their Applications in Modern Energy Systems

edited by Zhe Gao, Xiaoting Gao and Enchang Cui

submission deadline 15 Jul 2025 | Viewed by 477 | 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)

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 2025 | Viewed by 144 | 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)

Recent Computational Methods for Fractal and Fractional Nonlinear Partial Differential Equations

edited by

Kang-Jia Wang

and

Inés Tejado

submission deadline 31 Jul 2025 | Viewed by 34 | 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)

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 2026 | Viewed by 502 | 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)

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