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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 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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From Fractals to Fractional Calculus: Nonlinear Dynamics and Hybrid Complex Systems

edited by Katica (Stevanović) Hedrih

submission deadline 25 Dec 2025 | Viewed by 33 | Submission Open

Keywords: fractals; nonlinear dynamics; fractional calculus; mathematical phenomenology; hybrid systems; complex structures; discrete and continuous dynamic systems

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

Numerical Solution and Applications of Fractional Differential Equations, 3rd Edition

edited by

Libo Feng

Yang Liu

and

Lin Liu

submission deadline 25 Dec 2025 | Viewed by 32 | Submission Open

Keywords: numerical methods; mathematical modelling; fractional calculus; fractional differential equations; numerical analysis; fast algorithm

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

Fractional Calculus and Nonlinear Analysis: Theory and Applications

edited by

Wei-Shih Du

Marko Kostić

and

Daniel Velinov

submission deadline 31 Dec 2025 | 6 articles | Viewed by 9665 | 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)

Mathematical Inequalities in Fractional Calculus and Applications, 2nd Edition

edited by

Seth Kermausuor

and

Eze Nwaeze

submission deadline 31 Dec 2025 | 5 articles | Viewed by 4271 | 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)

Fractional Elliptic and Parabolic Equations: Analysis and Related Topics

edited by Wenxiong Chen and Leyun Wu

submission deadline 31 Dec 2025 | 2 articles | Viewed by 2061 | 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)

New Trends on Generalized Fractional Calculus, 2nd Edition

edited by

Milton Ferreira

Maria Manuela Fernandes Rodrigues

and

Nelson Felipe Loureiro Vieira

submission deadline 31 Dec 2025 | 2 articles | Viewed by 1986 | 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)

Applications of Fractional Calculus in Modern Mathematical Modeling

edited by

Feliz Manuel Minhós

Ali Raza

and

Muhammad Mohsin

submission deadline 31 Dec 2025 | 2 articles | Viewed by 714 | Submission Open

Keywords: fractional calculus; fractional differential equations (FDEs); fractional delay differential equations (FDDEs); stochastic fractional delay differential equations (SFDDEs); memory effects; fractional partial differential equations (FRDE's); stochastic fractional partial differential equations (SFPDEs); existence and uniqueness of solutions for FDEs; stability analysis of FDEs; sufficient conditions for solvability of FDEs with multi-point type data; uniqueness of solution for FDEs with impulses given by functions with several variables; solvability of functional FDES in involving P-Laplacian; multiplicity results for singular FDES in biological models; numerical methods in fractional calculus; biological systems modeling through fractional calculus; efficient computational methods to solve fractional differential equations for biological systems; control theory; mathematical modeling in finance through fractional calculus; data-driven approaches through fractional calculus; machine learning with fractional operators; future research directions and open problems in the application of fractional calculus in mathematical modeling

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

Applications of Fractional-Order Calculus in Robotics, 2nd Edition

edited by

Abhaya Pal Singh

and

Kishore Bingi

submission deadline 31 Dec 2025 | Viewed by 373 | Submission Open

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

Modeling and Dynamic Analysis of Fractional-Order Systems

edited by Li Ma and Fanhai Zeng

submission deadline 31 Dec 2025 | Viewed by 134 | Submission Open

Keywords: stability and control of fractional-order systems; reductions for fractional-order systems; bifurcation and chaos in fractional-order systems; discrete-time or continuous-time fractional-order systems; modeling via fractional calculus; generalized fractional calculus; numerical methods for fractional-order systems

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

Recent Trends in Computational Physics with Fractional Applications

edited by

Lanre Akinyemi

Mehmet Senol

Solomon Manukure

and Udoh Akpan

submission deadline 31 Dec 2025 | Viewed by 123 | Submission Open

Keywords: stability analysis; integral equations; semi-analytical method; traveling wave solutions; analytical and numerical methods; soliton theory and its applications; fractional calculus and its applications; ordinary and partial differential equations; symmetry analysis and conservation laws; mathematical modeling of flow in porous media; multi-scale approaches to modeling wave phenomena; high-order numerical differential formulas for fractional derivatives; numerical and computational methods in fractional differential equations

(This special issue belongs to the Section Mathematical Physics)

Nonlinear Fractional Differential Equation and Fixed-Point Theory, 2nd Edition

edited by

Mujahid Abbas

and

Talat Nazir

submission deadline 31 Dec 2025 | Viewed by 93 | Submission Open

Keywords: fixed point theory and its applications; approximation theory and its applications; variational inequality and its applications; fractional differential equations; iterated function system; fractal theory; differential equations; finite difference equations; nonlinear analysis; dynamical system; nonlinear convex analysis

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

Recent Advances in Fractional Differential Equations and Their Applications, 3rd Edition

edited by Xiaoli Chen,

Dongfang Li

and Ting Gao

submission deadline 31 Dec 2025 | Viewed by 90 | Submission Open

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

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

Applications of Fractal Dimensions in Rock Mechanics and Geomechanics

edited by

Hai Pu

and Kangsheng Xue

submission deadline 31 Dec 2025 | Viewed by 78 | Submission Open

Keywords: fractal dimension; rock mechanics; multiscale phenomena; fracture networks; nonlinear deformation; geomechanical applications

(This special issue belongs to the Section Engineering)

Advances in Fractional-Order Circuit Models: Theory and Applications

edited by

Chunhua Feng

submission deadline 31 Dec 2025 | Viewed by 74 | Submission Open

Keywords: fractional-order circuits; fractional-order models; fractional-order chaotic systems; fractional-order calculus; fractional-order oscillator

(This special issue belongs to the Section Complexity)

Modelling and Analysis of Fractional Behaviours: Alternative Approaches and Characterization

edited by

Jocelyn Sabatier

submission deadline 31 Dec 2025 | Viewed by 27 | Submission Open

Keywords: fractional behaviours; modelling; non-singular kernels; fractal

(This special issue belongs to the Section Engineering)

Fractal and Fractional in Geomaterials, 2nd Edition

edited by Yifei Sun

submission deadline 15 Jan 2026 | 2 articles | Viewed by 2822 | Submission Open

Keywords: fractal media; fractional mechanics; micro-to-macro. geomaterials; nonconventional approach

(This special issue belongs to the Section Engineering)

Fractional Dynamics in Epidemic Models: Theoretical Approaches and Applications

edited by

Qura Tul Ain

and

Anwarud Din

submission deadline 15 Jan 2026 | Viewed by 488 | Submission Open

Keywords: fractional calculus; fractional stochastic models; fractional dynamics; fractional-order epidemic models; epidemiological modeling; fractional models

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

Applications of Fractional-Order Grey Models, 2nd Edition

edited by

Lifeng Wu

and Shuli Yan

submission deadline 15 Jan 2026 | Viewed by 50 | Submission Open

Keywords: fractional-order; grey model; prediction; algorithm; application

(This special issue belongs to the Section Engineering)

Fractional Order Systems with Application to Electrical Power Engineering, 3rd Edition

edited by

Arman Oshnoei

and

Soroush Oshnoei

submission deadline 20 Jan 2026 | Viewed by 35 | Submission Open

Keywords: fractional order system; distributed energy resources; energy storage system; multi-energy systems; power electronic systems; power converters; renewable energy systems; artificial intelligence; stability analysis; intelligent control; fractional calculus; reliability and resiliency

(This special issue belongs to the Section Engineering)

Fractal Analysis in Biology and Medicine

edited by

Ivan Zaletel

submission deadline 30 Jan 2026 | 2 articles | Viewed by 1822 | Submission Open

Keywords: fractal analysis; fractal dimension; complexity; self-similarity; neuroscience; morphometry; cell and tissue analysis

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

Advances in Fractional-Order Chaotic and Complex Systems

edited by

Chunhua Wang

Fei Yu

and

Wei Yao

submission deadline 31 Jan 2026 | 4 articles | Viewed by 4163 | 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)

Fractional-Order Systems: Modeling and Control Applications in Engineering

edited by Jianwen Zhou and Tianwei Zhang

submission deadline 31 Jan 2026 | Viewed by 89 | Submission Open

Keywords: fractional-order differential or difference equations; fractional controlling theories; fractional-order systems; numerical methods; optimization techniques; complex networks; neural networks; applications in robotics and automation; applications in power and electrical systems; applications in mechanical systems; applications in biomedical engineering; applications in signal processing and communications

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

Fractional Calculus Applications for Signal Processing and Data Science

edited by

Héctor Vázquez-Leal

and

Manuel Duarte Ortigueira

submission deadline 15 Feb 2026 | Viewed by 101 | Submission Open

Keywords: fractional calculus; fractional transfer functions/Bode diagrams; fast numerical algorithms for fractional calculus; fractional signal processing in time and frequency domains; image processing and fractional techniques; embedded systems implementation of fractional operators; fractional filters design and implementation; fractional-order algorithms in AI; data science applications of fractional calculus; machine learning with fractional operators

Harmonic and Geometric Analysis for Fractional Equations

edited by Leandro Tavares and Alessio Fiscella

submission deadline 25 Feb 2026 | Viewed by 48 | Submission Open

Keywords: fractional equations; fractional operators; fractional derivatives; harmonic analysis; geometric analysis; regularity estimates; fractional Laplacian; geometric aspects of fractional equations; variational methods; existence of solutions; multiplicity

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

Fractal Analysis and Its Applications in Rock Engineering, Second Edition

edited by

Xiaohan Yang

Lihai Tan

and Gaofeng Liu

submission deadline 28 Feb 2026 | 1 articles | Viewed by 349 | 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)

Advances in Fractional Modeling and Computation, Second Edition

edited by

and

submission deadline 28 Feb 2026 | Viewed by 24 | Submission Open

Keywords: fractional models in natural sciences; fractional models in economics and engineering; numerical algorithms and discretization; fractional differential systems with control theory; fractional dynamic systems; analysis of fractional models; stochastic methods for fractional models; Monte Carlo methods; Markov chains and processes; stochastic modeling and simulation; related fractional models

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

Stochastic Models, Fractional Calculus and Non-Local Operators: Theoretical Results and Applications

edited by Enrica Pirozzi, Luisa Beghin, Janusz Gajda and Lauri Viitassari

submission deadline 1 Mar 2026 | Viewed by 78 | Submission Open

Keywords: statistical analysis of fractional models; fractional Brownian motion; fractional diffusion processes; fractional stochastic differential equations

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

Fractal Applications in Thermal Engineering

edited by Qingyong Zhu

submission deadline 10 Mar 2026 | Viewed by 21 | Submission Open

(This special issue belongs to the Section Engineering)

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

edited by

Martin Čech

submission deadline 14 Mar 2026 | 1 articles | Viewed by 1654 | 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)

Analysis and Applications of Fractional Calculus and Mathematical Modelling

edited by

Marcelo Kaminski Lenzi

submission deadline 31 Mar 2026 | 2 articles | Viewed by 1918 | 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)

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

edited by

Yi-Fei Pu

submission deadline 31 Mar 2026 | Viewed by 134 | 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)

Mathematical and Physical Analysis of Fractional Dynamical Systems, Second Edition

edited by Dimplekumar Chalishajar and Kasinathan Ravikumar

submission deadline 30 Apr 2026 | Viewed by 7 | 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)

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

edited by Rajarama Mohan Jena and

Snehashish Chakraverty

submission deadline 30 Apr 2026 | 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

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

edited by

Camillo Porcaro

submission deadline 1 May 2026 | 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)

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