Fractal and Fractional

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

edited by Ghulam Mujtaba, Saira Ashfaq and

submission deadline 9 Sep 2026 | 2 articles | Viewed by 2507 | 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 3919 | 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 3750 | 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 3239 | 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)

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

edited by

Gabriel Bengochea

and

Manuel Duarte Ortigueira

submission deadline 15 Sep 2026 | 4 articles | Viewed by 2953 | 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)

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 2919 | Submission Open

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

(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 | 5 articles | Viewed by 4610 | 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)

Fractal Approaches and Machine Learning in Financial Markets

edited by

Sun-Yong Choi

submission deadline 30 Sep 2026 | 4 articles | Viewed by 3759 | Submission Open

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

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 2961 | 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 2352 | 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)

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

edited by Zhiguo Luo and Danfeng Luo

submission deadline 30 Sep 2026 | 3 articles | Viewed by 1811 | 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)

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 1663 | 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 | 2 articles | Viewed by 1467 | 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)

Complexity, Fractals, and Nonlinear Phenomena Across Disciplines

edited by

Livio Conti

and Karolina Armonaite

submission deadline 30 Sep 2026 | 2 articles | Viewed by 1440 | 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 480 | 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 408 | 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 345 | 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 298 | 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 11083 | 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 4638 | 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 1177 | 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 12501 | 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 347 | 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 299 | 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 | 6 articles | Viewed by 11629 | 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 9797 | 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 8355 | 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)

Feature Papers for Mathematical Physics Section 2026

edited by

Haci Mehmet Baskonus

submission deadline 31 Oct 2026 | 7 articles | Viewed by 6089 | 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)

Recent Advances in Fractal Analysis for Hydrocarbon Dynamics and Flow Modeling

edited by

Meng Wang

and

Weidong Xie

submission deadline 31 Oct 2026 | 4 articles | Viewed by 5084 | Submission Open

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

Advances in Fractal Analysis for Financial Risk Assessment

edited by

Valentin Radu

and

Catalin Dumitrescu

submission deadline 31 Oct 2026 | 5 articles | Viewed by 3822 | 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 2895 | 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 1505 | 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 526 | 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 292 | 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 222 | 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 | 4 articles | Viewed by 2287 | 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 12618 | 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 | 8 articles | Viewed by 13375 | 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)

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 2573 | 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 1015 | 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)

Advances in Fractional-Order Control for Nonlinear Systems

edited by

Masoud Sotoodeh-Bahraini

and

Pedro Ferreira

submission deadline 16 Nov 2026 | 5 articles | Viewed by 4088 | 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)

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

edited by

Zunwei Fu

,

Bingzhao Li

and

Xiangyang Lu

submission deadline 25 Nov 2026 | 2 articles | Viewed by 1362 | 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 Order Systems with Application to Electrical Power Engineering, 3rd Edition

edited by

Arman Oshnoei

and

Soroush Oshnoei

submission deadline 30 Nov 2026 | 9 articles | Viewed by 11716 | 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)

Harmonic and Geometric Analysis for Fractional Equations

edited by Leandro Tavares and

Alessio Fiscella

submission deadline 30 Nov 2026 | 3 articles | Viewed by 4035 | 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 | 4 articles | Viewed by 2755 | 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)

Fixed Point Theory and Fractals, 2nd Edition

edited by

Cristina Serpa

,

Bilel Selmi

and

María A. Navascués

submission deadline 30 Nov 2026 | 2 articles | Viewed by 1474 | 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)

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

edited by Phumlani Dlamini and Simphiwe Simelane

submission deadline 30 Nov 2026 | 3 articles | Viewed by 1464 | 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)

Fractional and Fractal Methods with Their Mechanics Applications

edited by

Helvio Mollinedo

, Lucero Damián-Adame and

Didier Samayoa Ochoa

submission deadline 30 Nov 2026 | 2 articles | Viewed by 1369 | 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 Fractional-Order Memristive High-Dimensional Neural Networks: Dynamics, Synchronization, and Brain-Inspired Engineering Applications

edited by Jianying Xiao

submission deadline 30 Nov 2026 | 1 articles | Viewed by 705 | 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)

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 | 1 articles | Viewed by 562 | Submission Open

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

(This special issue belongs to the Section Engineering)

Journal Menu

Journal Browser

Special Issues

Further Information

Guidelines

MDPI Initiatives

Follow MDPI