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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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Fractional Order Modeling and Fault Detection in Complex Systems

edited by Li Wang

submission deadline 31 Oct 2026 | Viewed by 70 | Submission Open

Keywords: fractional-order system identification; data-driven detection; industrial anomaly detection; fractional neural operators; edge intelligence for monitoring; fractional-order digital twin-based fault detection; fractional-order digital signal processing algorithms

(This special issue belongs to the Section Complexity)

Fractional Operators and Symmetries in Mathematical Physics

edited by Felix Silva Costa and

Gastão Silves Ferreira Frederico

submission deadline 31 Oct 2026 | Viewed by 38 | Submission Open

Keywords: lie symmetries; fractional calculus; conservation law; fractional differential equation; similarity solution; mathematical physics

(This special issue belongs to the Section Mathematical Physics)

Recent Advances in the Spatial and Temporal Discretizations of Fractional PDEs, Second Edition

edited by

Xian-Ming Gu

, Hongbin Chen and

Xiangcheng Zheng

submission deadline 14 Nov 2026 | 8 articles | Viewed by 7093 | Submission Open

Keywords: fractional PDEs; finite difference; finite element; finite volume; spectral methods; nonuniform and adaptive discretizations; adaptive space– time methods; parallel-in-time methods; numerical methods; numerical treatments of integro-differential equations; nonlocal modeling and computation; convolution quadratures; modeling and simulations

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

Recent Advances in Fractional Fourier Transforms and Applications, 3rd Edition

edited by

Zunwei Fu

Bingzhao Li

and

Xiangyang Lu

submission deadline 25 Nov 2026 | Viewed by 23 | 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)

Fractional and Fractal Methods with Their Mechanics Applications

edited by

Helvio Mollinedo

, Lucero Damián-Adame and

Didier Samayoa Ochoa

submission deadline 30 Nov 2026 | Viewed by 257 | Submission Open

Keywords: fractals calculus; fractional calculus; fractal continuum; hurst exponent; cluster percolation; fractal dynamics; wave phenomena; time series; mechanical vibrations; thermal analysis

(This special issue belongs to the Section Mathematical Physics)

Multiscale Fractal Analysis in Unconventional Reservoirs, 2nd Edition

edited by

Yang Wang

and

Xiaowei Hou

submission deadline 30 Nov 2026 | Viewed by 137 | Submission Open

Keywords: multiscale fractal analysis; unconventional reservoirs; fractal geometry; fracture network characterization; pore structure analysis; fluid flow modeling; reservoir simulation; machine learning; digital rock physics

(This special issue belongs to the Section Engineering)

Connecting Quantum Computing and Fractal to Tackle Challenges in Medicine

edited by Consolato M. Sergi

submission deadline 30 Nov 2026 | Viewed by 64 | Submission Open

Keywords: quantum biology; quantum mechanics; biophysics; cancer; complexity; fractal characteristics; microstructures

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

Advances in Existence Theory and Stability of Variable Fractional Systems

edited by

Mustafa Avci

, Nguyen Thanh Chung, Shapour Heidarkhani and

Francisco Martinez

submission deadline 30 Nov 2026 | Viewed by 54 | Submission Open

Keywords: variable-order fractional derivatives; existence and uniqueness; stability analysis; lyapunov methods; fractional differential equations; time-varying systems; fixed point theory; asymptotic behavior; distributed-order models; nonlocal dynamics

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

Fractional Control Systems and Estimation: Control, State Observers and Parameter Estimation, 2nd Edition

edited by

Gustavo Ceballos-Benavides

and

Manuel A. Duarte-Mermoud

submission deadline 30 Nov 2026 | Viewed by 11 | Submission Open

Keywords: adaptive identification and control; robust control; PID control; parameter estimation; state observers

(This special issue belongs to the Section Engineering)

Numerical Solutions of Caputo-Type Fractional Differential Equations and Derivatives, Second Edition

edited by Phumlani Dlamini and Simphiwe Simelane

submission deadline 30 Nov 2026 | Viewed by 4 | Submission Open

Keywords: Caputo-type fractional differential equations; Caputo-type fractional derivatives; generalized fractional derivatives; fractional inequalities; fractional operator; fractional Green’ s functions; fractional Laplace transform; fractional evolution equations; finite difference schemes; spectral methods; existence and uniqueness; stability; controllability; iterative learning controls

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

Novel and Effective Applications of Fractional-Order Models

edited by

Carla M. A. Pinto

Cristina I. Muresan

and

Dana Copot

submission deadline 25 Dec 2026 | Viewed by 93 | Submission Open

Keywords: fractional calculus; fractional-order modeling; fractional-order control; FOPID controllers; fractional-order system identification; stability and robustness analysis; numerical implementation and approximation; real-world applications and experimental validation

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

Advances in Fractional Stochastic Differential Equations and Their Real-World Applications

edited by

Lu-Chuan Ceng

and Chingfeng Wen

submission deadline 30 Dec 2026 | Viewed by 1 | Submission Open

Keywords: fractional differential equations; stochastic differential equations; fractional-order dynamical systems; stochastic variational inequalities; fuzzy fractional differential inclusions; well-posedness analysis; hemivariational inequalities; controllability; optimality conditions; solvability or uniqueness

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

Modeling and Dynamic Analysis of Fractional-Order Systems

edited by Li Ma and Fanhai Zeng

submission deadline 31 Dec 2026 | 4 articles | Viewed by 3403 | 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)

Advances in Fractional Dynamics and Their Applications in Seismology

edited by

Jidong Yang

and Bingluo Gu

submission deadline 31 Dec 2026 | 1 articles | Viewed by 468 | Submission Open

Keywords: fractional wave equation; fractional laplacian; time-/space-domain fractional derivatives; seismic modeling; imaging; and inversion

(This special issue belongs to the Section Mathematical Physics)

Design and Applications of Fractional-Order Circuits and Filters

edited by

Dražen Jurišić

and

Costas Psychalinos

submission deadline 31 Dec 2026 | Viewed by 202 | Submission Open

Keywords: Cauer and Foster networks; fractional-order circuit theory; fractional-order control systems

(This special issue belongs to the Section Engineering)

Fractional Transform Methods in Complexity Analysis: Theory and Image Applications

edited by

Hao Zhang

submission deadline 31 Dec 2026 | Viewed by 82 | Submission Open

Keywords: complexity analysis; fractional theory; fractals theory; nonlinear dynamics; image encryption and coding; image compression; image watermarking and information hiding; image segmentation and processing; control and stability with complexities; AI methods in image processing

(This special issue belongs to the Section Complexity)

Fractional Order Modeling of Fluid Flow and Heat Transfer

edited by Razi Khan and

Zubair Ahmad

submission deadline 31 Dec 2026 | Viewed by 53 | Submission Open

Keywords: fractional calculus; fractional differential equations (FDEs); viscoelastic fluid flow; non-Newtonian fluids; nanofluids; hybrid and trihybrid fluids; heat and mass transfer; magnetohydrodynamics (MHD); computational fluid dynamics (CFD); fractional disease dynamics and epidemiological modelling; artificial neural networks (ANNs); physics-informed neural networks (PINNs)

(This special issue belongs to the Section Mathematical Physics)

Applications of Multifractal Analysis in Medical Signal and Image Processing

edited by

Nemanja Rajkovic

and

Nebojša T. Milošević

submission deadline 31 Dec 2026 | Viewed by 29 | Submission Open

Keywords: fractal analysis; multifractal analysis; morphometry; medical image analysis; biomedical signal processing; machine learning in medicine; computational biophysics

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

Fractional Calculus in Stochastic Systems, Game Theory and Decision Making

edited by Yoon-Tae Kim

submission deadline 31 Dec 2026 | Viewed by 7 | Submission Open

Keywords: fractional Brownian motion; fractional differential equation; fractional stochastic differential equation; fractional calculus; Malliavin calculus; long-range dependence; fractional differential games; fractional optimal control; fractional Markov decision processes

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

Fractal and Lacunarity Analysis of Time Series and Images: Foundations and Applications

edited by