Fractal and Fractional

Advances in Fractional Dynamics: Computational Approaches and Applications in Cosmology, Mechanics, and Complex Systems

edited by

submission deadline 31 Jul 2026 | Viewed by 619 | Submission Open

Keywords: fractional calculus; fractional dynamics; fractional differential equations; cosmology; gravitational systems; particle motion; classical and quantum mechanics; emergent structures in nonlinear and multifractal regimes; complex systems

(This special issue belongs to the Section Mathematical Physics)

Applications of Fractal Geometry in Surface Science

edited by

Henrique Duarte da Fonseca Filho

, Glenda Quaresma Ramos and

Robert S. Matos

submission deadline 31 Jul 2026 | Viewed by 351 | Submission Open

Keywords: fractal geometry; multifractals; surface roughness; biophysics; AFM/SEM/TEM in life sciences; morphological complexity; biomaterials; surface characterization; lacunarity; minkowski functionals

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

Fractal Geometry in Contact Mechanics: Characterization, Simulation and Real-World Applications

edited by

Rafael Schouwenaars

and

Carlos Figueroa

submission deadline 31 Jul 2026 | Viewed by 223 | Submission Open

Keywords: random fractal surfaces; contact mechanics; fractal dimension; multifractal surfaces; measurement and characterization; surface simulation; contact simulation; finite element method; boundary element method; elastoplastic behavior; viscoelastic behavior

(This special issue belongs to the Section Geometry)

Modeling and Inverse Problems of Nonlocal Phenomena

edited by Philipp Zimmermann

submission deadline 1 Aug 2026 | Viewed by 222 | Submission Open

Keywords: nonlocal partial differential equations; nonlinear fractional dynamical systems; anomalous diffusion models; nonlocal operators; Runge’ s approximation; nonlocal inverse problems

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

Recent Advances in Nonlocal Problems Involving the Fractional Laplacian Operators

edited by

Yun-Ho Kim

submission deadline 14 Aug 2026 | 6 articles | Viewed by 7082 | Submission Open

Keywords: fractional differential equations; fractional Sobolev spaces; variable exponent elliptic operator; fractional Laplacian problems with the external magnetic field; variational methods on the existence and multiplicity of solutions; a priori estimates and existence of solutions; uniqueness; non-existence; classifications of solutions; critical point theorem on the existence and multiplicity of solutions

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

Stochastic Dynamical Systems with Fractional Derivative: Theoretical Analysis and Numerical Simulation

edited by

Wei Li

and

Nataša Trišović

submission deadline 15 Aug 2026 | 2 articles | Viewed by 2053 | Submission Open

Keywords: fractional calculus; fractional integration; fractional derivative; stochastic dynamical systems; stabilization; system response; fractional-order controller

(This special issue belongs to the Section Engineering)

Nonlinear Dynamics, Chaos and Control of Fractional Systems

edited by Vinícius Piccirillo,

José Manoel Balthazar

,

Angelo Marcelo Tusset

and Jeferson José de Lima

submission deadline 15 Aug 2026 | 2 articles | Viewed by 1847 | Submission Open

Keywords: fractional-order systems; nonlinear dynamics; chaos and bifurcation; fractional-order control; memory effects; time series modeling

(This special issue belongs to the Section Engineering)

Fractional Calculus, Artificial Intelligence and Complexity Analysis in Neurological and Chaotic Systems

edited by

Ricardo Zavala-Yoé

,

Jorge Mario Cruz-Duarte

, Milan Stehlik and

Porfirio Toledo Hernández

submission deadline 15 Aug 2026 | Viewed by 397 | Submission Open

Keywords: fractional calculus; neurological systems; artificial intelligence; chaotic dynamics; fractal dimension; entropy measures; EEG/ECoG signal processing; neuroimaging analysis; time series analysis; brain complexity

Advances in Fractional Initial and Boundary Value Problems

edited by

Sotiris K. Ntouyas

,

Bashir Ahmad

and

Jessada Tariboon

submission deadline 20 Aug 2026 | 7 articles | Viewed by 5887 | Submission Open

Keywords: qualitative properties of the solutions (positivity; oscillation; asymptotic behavior; stability; etc.); topological methods in differential equations and inclusions; approximation of the solutions; eigenvalue problems; variational methods; fixed point theory; critical point theory; applications to real-world phenomena

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

Fractional-Order Dynamics in AI: Neural Networks and Applications

edited by

Eva H. Dulf

submission deadline 20 Aug 2026 | 1 articles | Viewed by 1417 | Submission Open

Keywords: fractional-order calculus; artificial intelligence; neural networks; machine learning; nonlinear dynamics; memory effects; optimisation; deep learning

(This special issue belongs to the Section Engineering)

Fractional-Order Controllers in Electronics and Automation Engineering, 2nd Edition

edited by

Allan G.S. Sánchez

and Joaquin Alvarez

submission deadline 30 Aug 2026 | Viewed by 229 | 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)

Fractional and Fractal Methods in Biomedical Imaging and Time Series Learning

edited by

Ziyang Wang

, Chengjun Wang and

Jiabao Li

submission deadline 31 Aug 2026 | 9 articles | Viewed by 16565 | Submission Open

Keywords: fractional calculus; medical robotic control; biomedical signal processing; medical image analysis; time series machine learning

(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 N. Chalishajar and Kasinathan Ravikumar

submission deadline 31 Aug 2026 | 9 articles | Viewed by 8445 | 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)

Applications of Fractal Dimensions in Rock Mechanics and Geomechanics

edited by

Hai Pu

and Kangsheng Xue

submission deadline 31 Aug 2026 | 7 articles | Viewed by 8242 | Submission Open

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

(This special issue belongs to the Section Engineering)

Analysis and Applications of Fractional Calculus in Computational Physics

edited by

Slobodanka Galovic

and

Dalibor Chevizovich

submission deadline 31 Aug 2026 | 4 articles | Viewed by 4161 | Submission Open

Keywords: fractional calculus in physics; fractional operators; integral transformations of irrational functions; inverse Laplace transform of irrational functions; time-delayed fractional models; numerical methods in fractional problems

(This special issue belongs to the Section Mathematical Physics)

Fractal Analysis and Fractal Dimension in Materials Chemistry, 2nd Edition

edited by

Gianina Dobrescu

,

Florica Papa

and

Razvan State

submission deadline 31 Aug 2026 | 1 articles | Viewed by 2443 | Submission Open

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

Hybrid Modeling Approaches: Deep Learning and Fractional Differential Equations in Complex Systems

edited by

Ali Turab

,

Josue Antonio Nescolarde Selva

and Andres Montoyo

submission deadline 31 Aug 2026 | 1 articles | Viewed by 1352 | Submission Open

Keywords: fractional differential equations (FDEs); fractional difference equations; fractional physics-informed neural networks (fPINNs); deep learning for dynamical systems; Fourier neural operators (FNOs); nonlocal and memory-dependent models; variable-order differential equations; fractal-fractional order mathematical models; time-fractional and space-fractional models; hybrid neural– stochastic modeling; inverse problems in fractional systems; reinforcement learning in fractional systems; cognitive modeling with FDEs; multiscale modeling in complex systems; deep neural network solvers for FDEs; applications in biology and neuroscience; computational and stability methods in fractional calculus

(This special issue belongs to the Section Optimization, Big Data, and AI/ML)

Bifurcation, Chaos, and Fractals in Fractional-Order Electrical and Electronic Systems, 2nd Edition

edited by Faqiang Wang,

Shaobo He

and Hongbo Cao

submission deadline 31 Aug 2026 | 2 articles | Viewed by 1283 | Submission Open

Keywords: bifurcation and its control chaos and its control; fractals and their control; fractional-order inductor/capacitor; fractional-order memristor/meminductor/memcapacitor; fractional-order circuits and systems; fractional-order electrical and electronic systems; multi-timescale and entropy analysis; fractional calculus applications

Application of Fractal Processes and Fractional Derivatives in Finance, 3rd Edition

edited by Leunglung Chan

submission deadline 31 Aug 2026 | 1 articles | Viewed by 1136 | Submission Open

Keywords: rough volatility model; fractal processes applied in finance and other fields; fractional differential equations; fractional diffusions; fractional calculus; transform methods applied to fractional differential equations; numerical methods for fractional partial differential equations; fractional operators

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

Fractal and Fractional Order Modeling of Real-World Phenomena

edited by

Stefan Balint

submission deadline 31 Aug 2026 | Viewed by 289 | Submission Open

Keywords: Mandelbrot's fractals; discrete difference equations; fractional order continuous differential equations; mathematical modeling; real-world systems; continuous and discrete models; fractional calculus

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

Advances in Fractional Kinetic Models and Their Practical Applications

edited by

Ana Caroline Raimundini Aranha

and Gioacchino Alotta

submission deadline 31 Aug 2026 | Viewed by 228 | Submission Open

Keywords: fractional calculus; fractional kinetics; anomalous diffusion; nonlocal models; memory effects; numerical methods; fractional dynamic systems; applied fractional modelling

(This special issue belongs to the Section Mathematical Physics)

Multifractal Techniques (MF-DFA) and Its Applications in Financial and Economic Complexity

edited by Ghulam Mujtaba, Saira Ashfaq and

Jawad Syed Shahzad

submission deadline 9 Sep 2026 | 1 articles | Viewed by 1314 | Submission Open

Keywords: MF-DFA; multifractality; MF-DCCA; asymmetric scaling; financial complexity; volatility dynamics; contagion; data analytics; market efficiency; cross-correlation

(This special issue belongs to the Section Complexity)

Fractal Theory and Models in Nonlinear Dynamics and Their Applications, 2nd Edition

edited by

Luis Manuel Palacios-Pineda

and

Oscar Martínez-Romero

submission deadline 15 Sep 2026 | 3 articles | Viewed by 3387 | Submission Open

Keywords: fractal theory; multifractals; fractal– fractional calculus; fractional chaotic systems; fractional nonlinear dynamics

(This special issue belongs to the Section Mathematical Physics)

Multifractal Analysis and Complex Systems

edited by

Enrico De Santis

and Alessio Martino

submission deadline 15 Sep 2026 | 3 articles | Viewed by 2520 | Submission Open

Keywords: multifractal analysis; fractal geometry; self-affine systems; complex systems; scaling laws; nonlinear dynamics; neural networks; network science; applied mathematics

(This special issue belongs to the Section Complexity)

Modeling, Simulation and Applications of Fractal/Fractional Calculus to Engineering Materials

edited by

Wei Cai

,

Xianglong Su

and

Wojciech Sumelka

submission deadline 15 Sep 2026 | 1 articles | Viewed by 2287 | Submission Open

Keywords: constitutive models; fractional/fractal viscoelasticity; fractional/fractal viscoplasticity; numerical methods; multiscale modeling; dynamic analyses; artificial intelligence (AI)

(This special issue belongs to the Section Engineering)

Theoretical and Numerical Methods for Fractional and Nonlocal Partial Differential Equations

edited by

Giuseppe Di Fazio

and Giovanni Molica Bisci

submission deadline 15 Sep 2026 | 3 articles | Viewed by 1983 | Submission Open

Keywords: nonlocal equations; fractional models; numerical methods; variational methods; regularity theory

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

Continuous/Discrete-Time Fractional Systems: Modelling, Design and Estimation, 2nd Edition

edited by

Gabriel Bengochea

and

Manuel Duarte Ortigueira

submission deadline 15 Sep 2026 | 2 articles | Viewed by 1376 | Submission Open

Keywords: autoregressive-moving average (ARMA); shift-invariant; scale-invariant; fBm; Liouville; Liouville– Caputo; Hadamard; Riemann– Liouville; Dzherbashian– Caputo; Grunwald– Letnikov; two-sided Riesz– Feller derivatives

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

Fractal and Fractional in Geotechnical Engineering, Second Edition

edited by Shao-Heng He, Zhi Ding and

Panpan Guo

submission deadline 30 Sep 2026 | 2 articles | Viewed by 2889 | Submission Open

Keywords: fractal dimension; fractional-order mechanics; micro-to-Macro analysis; geomaterial; tunnel; rock; concrete; foamed light soil; bituminous mixture

(This special issue belongs to the Section Engineering)

Fractional Nonlinear Dynamics in Science and Engineering

edited by

Jorge E. Macías Díaz

and

Tassos Bountis

submission deadline 30 Sep 2026 | 2 articles | Viewed by 2061 | Submission Open

Keywords: nonlinear fractional models; deterministic and stochastic models; fractional nonlinear systems; dynamics of fractional nonlinear systems; complex systems

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

Boundary Value Problems for Nonlinear Fractional Differential Equations: Theory, Methods and Application, Second Edition

edited by

Wenying Feng

and Feng Gao

submission deadline 30 Sep 2026 | 2 articles | Viewed by 1699 | Submission Open

Keywords: boundary value problems; eigenvalue problems; existence and positivity of solutions; uniqueness and multiplicity of solutions; stability and equilibrium; numerical solutions; fixed point methods and applications; nonlinear differential and difference equations; modeling with FDEs; neural networks and FDEs; fractional q-differential equations

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

Fractal Approaches and Machine Learning in Financial Markets

edited by

Sun-Yong Choi

submission deadline 30 Sep 2026 | 3 articles | Viewed by 1446 | Submission Open

Keywords: fractal and multifractal analysis; machine learning; deep learning; financial market; volatility; risk management; portfolio optimization; asset pricing; financial decision-making

Fractional Calculus in Bioengineering and Mathematical Biology: Novel Approaches to Biomedical Applications and Infectious Disease Dynamics

edited by

Andrew Omame

submission deadline 30 Sep 2026 | 1 articles | Viewed by 1195 | Submission Open

Keywords: fractional dynamics; bioengineering; biomedical applications; epidemic modeling; mathematical biology; fractional differential equations; computational modeling; anomalous diffusion; memory effects in biology

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

Calculus of Variations, Fractional Calculus and Their Applications

edited by

Matheus J. Lazo

submission deadline 30 Sep 2026 | 1 articles | Viewed by 936 | Submission Open

Keywords: fractional calculus of variations; fractional derivatives and integrals; necessary and sufficient optimality conditions; fractional Euler– Lagrange equation; numerical and analytical methods; applications of fractional calculus of variations

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

Analysis of Fractional Stochastic Differential Equations and Their Applications, Second Edition

edited by Zhiguo Luo and Danfeng Luo

submission deadline 30 Sep 2026 | 2 articles | Viewed by 904 | Submission Open

Keywords: fractional differential equations; stochastic differential equations; delay differential equations; impulsive differential equations; fuzzy differential equations; stability analysis; averaging principle; controllability; averaging principle; existence or uniqueness

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

Complexity, Fractals, and Nonlinear Phenomena Across Disciplines

edited by

Livio Conti

and Karolina Armonaite

submission deadline 30 Sep 2026 | 1 articles | Viewed by 575 | Submission Open

Keywords: fractal analysis; non-linear measures; statistical analysis; uncertainty estimates; information theory; complex systems; neuroscience; astrophysics; particle physics

(This special issue belongs to the Section Mathematical Physics)

Emergent Structures and Asymptotic Analysis from Local Dynamics of Discrete Models

edited by

Mariusz Białecki

and Yohei Tutiya

submission deadline 30 Sep 2026 | Viewed by 380 | Submission Open

Keywords: fractals; self-similar structures; complex systems; discrete models; nonlinear dynamical systems; cellular automata; analytical methods; combinatorial methods; discrete nonlinear equations; percolation theory; network dynamics; nonlinear system and applied in physics; computational modelling; discrete integrable systems

Fractional Fourier Transform for Optical Signal and Image Processing

edited by

Pedro Chamorro-Posada

submission deadline 30 Sep 2026 | Viewed by 255 | Submission Open

Keywords: theoretical foundations; discrete and fast computational algorithms; optical system modeling and simulation; optical signal processing applications; image processing and computational imaging; quantum optics and quantum information applications of FrFT

Advances in Fractional Heat Conduction and Its Applications

edited by

Marica N. Popovic

,

Slobodanka Galovic

and

Miroslava Jordovic Pavlovic

submission deadline 30 Sep 2026 | Viewed by 221 | Submission Open

Keywords: fractional heat conduction theory; thermal transport; mathematical formulation; analytical and numerical solutions; micro- and nanoscale systems; thermal-wave interferometry

(This special issue belongs to the Section Mathematical Physics)

Advances in Fractional Evolution Equations: Periodicity and Stability

edited by Gaston M. N'Guérékata

submission deadline 30 Sep 2026 | Viewed by 175 | Submission Open

Keywords: fractional evolution equations; periodic-type solutions; stability; controllability; attractivity

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

Fractional Order Modelling of Dynamical Systems

edited by

Zubair Ahmad

submission deadline 15 Oct 2026 | 6 articles | Viewed by 8201 | Submission Open

Keywords: fractional derivatives; numerical methods of fractional order systems; fractional dynamical systems; stability analysis; fractional models in fluid dynamics; disease dynamics and epidemiology; fractional modelling with applications

(This special issue belongs to the Section Engineering)

Fractals in Physiology and Medicine

edited by

Igor V. Pantic

submission deadline 15 Oct 2026 | 2 articles | Viewed by 3463 | Submission Open

Keywords: fractal analysis; physiological signals; biomedical imaging; machine learning in physiology; complex systems; computational physiology

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

Modeling, Optimization, and Control of Fractional-Order Neural Networks and Nonlinear Systems, Second Edition

edited by

Kaibo Shi

,

Zhinan Peng

, Xin Wang and

Xiao Cai

submission deadline 17 Oct 2026 | 1 articles | Viewed by 856 | Submission Open

Keywords: fractional order neural networks; nonlinear systems; networked control systems; modelling and analysis; control and optimization; intelligent learning; multiagent systems

(This special issue belongs to the Section Engineering)

Fractional Calculus Applications for Signal Processing and Data Science

edited by

Héctor Vázquez-Leal

and

Manuel Duarte Ortigueira

submission deadline 30 Oct 2026 | 2 articles | Viewed by 11301 | 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

Fractal (Self-Similar) Porous Media: Modeling and Applications

edited by

Zine El Abiddine Fellah

, Kouqi Liu and Abdellah Bouchendouka

submission deadline 30 Oct 2026 | Viewed by 177 | Submission Open

Keywords: transport phenomena; fractal theory; porous media; self-similar

(This special issue belongs to the Section Engineering)

Fractional-Order Delayed Neural Networks: Bifurcation Analysis and Dynamic Behaviors

edited by

Maoxin Liao

and Mingshu Peng

submission deadline 30 Oct 2026 | Viewed by 174 | Submission Open

Keywords: fractional-order neural networks; delayed systems; stability; bifurcation theory; fractional-order controller; chaos control; synchronization

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

Fractal Functions: Theoretical Research and Application Analysis

edited by Yong-Shun Liang and Jia Liu

submission deadline 31 Oct 2026 | 5 articles | Viewed by 9343 | Submission Open

Keywords: iterated function systems; fractal interpolation functions; fractal functions; fractal surfaces; fractional calculus; function spaces; self-similar sets and measures; self-affine and self-conformal sets/measures; fractal approximation and modeling; quantization dimension; box dimension; Hausdorff dimension; and L^q dimensions; applications of the fractal functions to any areas of finance; engineering; economy; biology; etc.

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

Applied Fractional Calculus in Machine Learning and Biomedical Engineering

edited by

Saptarshi Das

submission deadline 31 Oct 2026 | 2 articles | Viewed by 8521 | Submission Open

Keywords: fractional-order machine learning algorithms; application of fractional calculus in deep learning; including novel architectures and training methods; fractional calculus in biomedical signal processing (EEG; ECG; MRI; etc.); modelling of biological phenomena using fractional differential equations; fractional-order control systems in biomedical devices; fractional calculus in the analysis of biomedical data and its integration with ML techniques; comparative studies between integer-order and fractional-order methods in ML and BME; practical challenges in applying FC to real-world problems in ML and BME

(This special issue belongs to the Section Optimization, Big Data, and AI/ML)

Fractional-Order Modeling and Control for Complex Dynamic Systems: Methodologies and Applications

edited by Necdet Sinan Özbek,

Ying Luo

and

Yangquan Chen

submission deadline 31 Oct 2026 | 7 articles | Viewed by 5912 | Submission Open

Keywords: fractional-order systems; fractional calculus; complex dynamic systems; fractional-order control; non-integer order modeling; robust control; adaptive control; sliding mode control; stability analysis; system identification; memory and hereditary systems; numerical methods for fractional systems; networked and distributed systems; machine learning in fractional control; biomedical applications of fractional models; energy systems modeling; optimization in fractional-order systems; time-domain and frequency-domain analysis

(This special issue belongs to the Section Engineering)

Recent Advances in Fractal Analysis for Hydrocarbon Dynamics and Flow Modeling

edited by

Meng Wang

and

Weidong Xie

submission deadline 31 Oct 2026 | 3 articles | Viewed by 3680 | Submission Open

Keywords: fractal and fractional theory; fractal characteristics; gas dynamics; flow modeling; CO2 sequestration; pore structure; unconventional reservoirs; oil and gas migration

Feature Papers for Mathematical Physics Section 2026

edited by

Haci Mehmet Baskonus

submission deadline 31 Oct 2026 | 4 articles | Viewed by 2762 | Submission Open

Keywords: engineering problems; analytical methods; numerical methods; computational mathematics; nonlinear system and applied in physics; information science; communications theory; bioinformatics; health problems; networks; physics; engineering and applied sciences; economy; statistics; fractals; fractional calculus; nonlinear dynamical systems; graph theory; statistical learning theory; computation topics on energy and environmental science; artificial intelligence; data science; discrete dynamical system

(This special issue belongs to the Section Mathematical Physics)

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