Fractal and Fractional

Advances in Fractal Analysis for Financial Risk Assessment

edited by

and

submission deadline 31 Oct 2026 | 2 articles | Viewed by 2477 | Submission Open

Keywords: fractal analysis; fractional processing; financial risk assessment; multifractality in financial markets; systemic risk; machine learning and fractals; volatility modeling and prediction

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

Fractional Order Modeling and Fault Detection in Complex Systems

edited by Li Wang

submission deadline 31 Oct 2026 | 2 articles | Viewed by 2419 | 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)

Fractal Dimensions and Their Implications in Characterization of Porous Media

edited by

Boming Yu

, Boqi Xiao and

Dahua Shou

submission deadline 31 Oct 2026 | 1 articles | Viewed by 1237 | Submission Open

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

(This special issue belongs to the Section Engineering)

Numerical Simulations of Dynamic Behaviors and Control Design in Fractional Engineering Applications

edited by

José Manoel Balthazar

,

Angelo Marcelo Tusset

,

Hugo Valadares Siqueira

and Jeferson José de Lima

submission deadline 31 Oct 2026 | Viewed by 432 | Submission Open

Keywords: fractional calculus; numerical simulations; dynamic behaviors; control design; sensitivity analysis; fractional programming; fractional-order systems; optimization techniques

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

Fractional Operators and Symmetries in Mathematical Physics

edited by Felix Silva Costa and

Gastão Silves Ferreira Frederico

submission deadline 31 Oct 2026 | Viewed by 153 | 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)

Fractional Calculus and Fractals in Colloidal and Soft Matter Systems

edited by

Noushin Raeisi Kheirabadi

submission deadline 31 Oct 2026 | Viewed by 113 | Submission Open

Keywords: fractional calculus; colloids and soft matter; anomalous diffusion; memory effects in materials

(This special issue belongs to the Section Mathematical Physics)

Advances in Boundary Value Problems for Fractional Differential Equations, 4th Edition

edited by

Rodica Luca

submission deadline 10 Nov 2026 | 3 articles | Viewed by 1484 | 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)

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 10881 | 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)

Applications of General Fractional Calculus Models: Insights into Viscoelasticity and Wave Propagation

edited by Yiying Feng,

Jiangen Liu

, Yiming Wang and

Alex Elías-Zúñiga

submission deadline 15 Nov 2026 | 7 articles | Viewed by 11245 | Submission Open

Keywords: general fractional calculus; integration of mathematics and engineering; fractional rheological models; fractal dimensional space; nonlinear theory; fractional wave propagation models

(This special issue belongs to the Section Engineering)

Advances in Fractional-Order Control for Nonlinear Systems

edited by

Masoud Sotoodeh-Bahraini

and

Pedro Ferreira

submission deadline 15 Nov 2026 | 3 articles | Viewed by 1936 | 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)

Artificial Intelligence and Fractional Modelling for Energy Systems

edited by

Alejandro Ramos Martín

and

Federico León Zerpa

submission deadline 15 Nov 2026 | 2 articles | Viewed by 1883 | 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)

Advances in Fractional Order Signal Processing: Theory and Methods

edited by Yuan-Min Li and Deyun Wei

submission deadline 15 Nov 2026 | 1 articles | Viewed by 797 | 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)

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

edited by

Zunwei Fu

,

Bingzhao Li

and

Xiangyang Lu

submission deadline 25 Nov 2026 | 1 articles | Viewed by 791 | 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)

Harmonic and Geometric Analysis for Fractional Equations

edited by Leandro Tavares and

Alessio Fiscella

submission deadline 30 Nov 2026 | 2 articles | Viewed by 3009 | 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)

Multiscale Fractal Analysis in Unconventional Reservoirs, 2nd Edition

edited by

Yang Wang

and

Xiaowei Hou

submission deadline 30 Nov 2026 | 3 articles | Viewed by 1249 | 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)

Fractional and Fractal Methods with Their Mechanics Applications

edited by

Helvio Mollinedo

, Lucero Damián-Adame and

Didier Samayoa Ochoa

submission deadline 30 Nov 2026 | 1 articles | Viewed by 972 | 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)

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 284 | 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)

Connecting Quantum Computing and Fractal to Tackle Challenges in Medicine

edited by Consolato M. Sergi

submission deadline 30 Nov 2026 | Viewed by 258 | Submission Open

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

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

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 255 | 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)

Fixed Point Theory and Fractals, 2nd Edition

edited by

Cristina Serpa

,

Bilel Selmi

and

María A. Navascués

submission deadline 30 Nov 2026 | Viewed by 210 | Submission Open

Keywords: fixed point theorems; fractal sets; functions and measures; fixed-point approximation and stability; iterative methods for the solution of differential and integral equations; iterated function systems; discrete dynamical systems; fractional calculus related to fixed point theory; dynamical systems or deterministic/stochastic fractals; the applications of these above fields; multifractal analysis; fractal geometry; dynamical systems and ergodic theory

(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 205 | Submission Open

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

(This special issue belongs to the Section Engineering)

Advances in Fractional-Order Memristive High-Dimensional Neural Networks: Dynamics, Synchronization, and Brain-Inspired Engineering Applications

edited by Jianying Xiao

submission deadline 30 Nov 2026 | Viewed by 121 | Submission Open

Keywords: fractional-order systems; intelligent control; neural networks; memristive systems; stability analysis; synchronization; lyapunov method

(This special issue belongs to the Section Engineering)

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

edited by Katica (Stevanović) Hedrih

submission deadline 10 Dec 2026 | 5 articles | Viewed by 4498 | 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)

Fractal Analysis and Its Applications in Rock Engineering, Second Edition

edited by

Xiaohan Yang

,

Lihai Tan

and Gaofeng Liu

submission deadline 15 Dec 2026 | 8 articles | Viewed by 9221 | 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)

Fractional Elliptic and Parabolic Equations: Analysis and Related Topics

edited by Wenxiong Chen and Leyun Wu

submission deadline 18 Dec 2026 | 3 articles | Viewed by 4058 | 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)

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 | 1 articles | Viewed by 813 | 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 Order Systems and Robust Control, 3rd Edition

edited by

Feng Liu

submission deadline 25 Dec 2026 | 1 articles | Viewed by 724 | Submission Open

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

(This special issue belongs to the Section Engineering)

Fractal and Fractional Analysis in Biomedical Sciences and Engineering, 2nd Edition

edited by

Andjelija Ž. Ilić

and

Corina S Drapaca

submission deadline 30 Dec 2026 | Viewed by 687 | 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

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

edited by

Lu-Chuan Ceng

and Ching‑Feng Wen

submission deadline 30 Dec 2026 | Viewed by 220 | 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)

Recent Trends in Computational Physics with Fractional Applications

edited by

Lanre Akinyemi

,

Mehmet Senol

,

Solomon Manukure

and Udoh Akpan

submission deadline 31 Dec 2026 | 5 articles | Viewed by 5934 | 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)

Modeling and Dynamic Analysis of Fractional-Order Systems

edited by Li Ma and Fanhai Zeng

submission deadline 31 Dec 2026 | 5 articles | Viewed by 5483 | 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)

Fractional Transform Methods in Complexity Analysis: Theory and Image Applications

edited by

Hao Zhang

submission deadline 31 Dec 2026 | 2 articles | Viewed by 1626 | 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)

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 1178 | 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)

Fractional Modeling and Dynamics Analysis of Complex Systems

edited by

Chao Fu

,

Yunpeng Zhu

and Kuan Lu

submission deadline 31 Dec 2026 | 2 articles | Viewed by 643 | Submission Open

Keywords: fractional order modeling; complex dynamical systems; statistical characteristics; computational methods of fractional mechanics; fractional order stiffness and damping effects in mechanical systems; propagation of uncertainty in complex dynamical systems; fractal surface topology in contact mechanics; development of solution methods for fractional nonlinear systems

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

Design and Applications of Fractional-Order Circuits and Filters

edited by

Dražen Jurišić

and

Costas Psychalinos

submission deadline 31 Dec 2026 | Viewed by 479 | Submission Open

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

(This special issue belongs to the Section Engineering)

Advances in Fractal and Fractional Dynamics

edited by

Carlo Cattani

and

Haci Mehmet Baskonus

submission deadline 31 Dec 2026 | Viewed by 383 | Submission Open

Keywords: fractional calculus; fractal geometry; nonlocal dynamics; complex systems; fractional PDEs; stochastic processes; multiscale modeling; network dynamics

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

edited by

Erveton Pinheiro Pinto

and

Marcelo Pires

submission deadline 31 Dec 2026 | Viewed by 247 | Submission Open

Keywords: lacunarity; fractality; time series; images; data science

(This special issue belongs to the Section Complexity)

Fractal and Fractional Modelling in Deep Mining and Geomechanics

edited by Teng Teng,

Yi Xue

and Zhengzheng Cao

submission deadline 31 Dec 2026 | Viewed by 236 | Submission Open

Keywords: rock mechanics and rock engineering; fractal geometry and dimension; fractional calculus and constitutive models; pore structure and permeability; deep mining and geomechanics; multi-physics coupling; rock damage and fracture

(This special issue belongs to the Section Engineering)

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 227 | 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 Order Modeling of Fluid Flow and Heat Transfer

edited by Razi Khan and

Zubair Ahmad

submission deadline 31 Dec 2026 | Viewed by 192 | 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)

Fractional Calculus in Stochastic Systems, Game Theory and Decision Making

edited by Yoon-Tae Kim

submission deadline 31 Dec 2026 | Viewed by 170 | 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)

Recent Advances in Fixed Point Theory and Applications to Fractional Differential Equations

edited by Jamshaid Ahmad and

Maggie Aphane

submission deadline 1 Jan 2027 | 1 articles | Viewed by 763 | Submission Open

Keywords: fixed point theory; fractional differential equations; generalized metric spaces; generalized contractions; integral and integro-differential equations; stability analysis; applications of fractional calculus

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

Advances in Fractional Modeling and Computation, Second Edition

edited by

,

,

and

submission deadline 15 Jan 2027 | 4 articles | Viewed by 5617 | 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)

Fractional-Order Systems: Modeling and Control Applications in Engineering

edited by

Jianwen Zhou

and

Tianwei Zhang

submission deadline 15 Jan 2027 | 3 articles | Viewed by 3392 | 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-Order Modeling in Data-Driven Intelligent Systems: From Optimization to AI/ML Applications

edited by Yan Li and Ziquan Yu

submission deadline 15 Jan 2027 | 1 articles | Viewed by 529 | 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)

Fractional Calculus with Applications in Rock Mechanics and Mining Engineering

edited by

Shuai Yang

and

Cun Zhang

submission deadline 31 Jan 2027 | 2 articles | Viewed by 1137 | Submission Open

Keywords: fractional calculus; fractional modelling; fractional-order evolution; fractional-order image recognition and reconstruction; fractional-order AI/deep mining; fractional-order multiphysics coulping methods; fractional signal/information processing; rock dynamics; rock mechanics; mining engineering; deep mining

(This special issue belongs to the Section Engineering)

Emerging Trends in Fractal Geometry and Dynamic Systems

edited by

Mrinal Kanti Roychowdhury

, Zhiming Li, Megha Pandey and

María A. Navascués

submission deadline 31 Jan 2027 | 1 articles | Viewed by 812 | Submission Open

Keywords: fractal geometry; multifractal analysis; geometric analysis; dynamical systems; fractal models; fractal sets; ergodic theory; measure theory

(This special issue belongs to the Section Geometry)

Advances in Fractional Integral Inequalities: Theory and Applications, Second Edition

edited by

Armando Gallegos

and

Jorge E. Macías Díaz

submission deadline 31 Jan 2027 | 1 articles | Viewed by 229 | Submission Open

Keywords: fractional integral inequalities; numerical integrations methods; operator theory; convex and concave functions.

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

Fractal and Fractional Approaches in Interdisciplinary Mechanics

edited by Yajun Yin and

Zhimo Jian

submission deadline 31 Jan 2027 | Viewed by 216 | Submission Open

Keywords: fractal theory; fractional calculus; interdisciplinary mechanics; nonconventional approach; nonlinear mechanical behavior; local fractional operators; multi-scale characterization; memory-dependent effects; engineering applications

(This special issue belongs to the Section Engineering)

Analysis and Modeling of Fractional-Order Dynamical Networks, Second Edition

edited by Fei Wang and

Feifei Du

submission deadline 31 Jan 2027 | Viewed by 158 | Submission Open

Keywords: fractional-order systems; neural networks; gene regulatory networks; dynamical networks; multi-agent systems; coupled systems; synchronization control; heterogeneous networks; analysis of dynamic behavior

(This special issue belongs to the Section Complexity)

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