Fractal and Fractional

Advances in Fractional-Order PID Control: Theory and Applications

edited by

and César-Fernando Méndez-Barrios

submission deadline 30 Jun 2026 | Viewed by 235 | Submission Open

Keywords: fractional systems; PID control; control theory; chaotic dynamics; automatic control; real-world applications; time-delay systems

(This special issue belongs to the Section Engineering)

Computational and Analytical Approaches in Fractional Calculus for Big Data and Digital Twins

edited by

Cecília Coelho

, Maria Fernanda Pires da Costa and

Luís Lima Ferrás

submission deadline 30 Jun 2026 | Viewed by 179 | Submission Open

Keywords: fractional calculus; fractional differential equations; computational modeling; numerical methods; machine learning; big data; digital twins; engineering; physics

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

Multifractal Phenomena in Turbulence

edited by Alexander A. Migdal

submission deadline 30 Jun 2026 | Viewed by 165 | Submission Open

Keywords: turbulence theory; multifractal phenomena; microscopic theory; phenomenological modeling; numerical simulation; experimental validation

(This special issue belongs to the Section Complexity)

Complexity, Fractality and Fractional Dynamics Applied to Science and Engineering, 2nd Edition

edited by Alexandra M. S. F. Galhano,

António Lopes

and

Sergio Adriani David

submission deadline 30 Jun 2026 | Viewed by 132 | Submission Open

Keywords: fractional-order systems; memory; econophysics; time series; finance; economics; big data; complex systems; biosystems; fractals

(This special issue belongs to the Section Complexity)

Fractal and Fractional Modelling Applied to Energy Storage

edited by Mei Yin and

Guozhu Zhang

submission deadline 30 Jun 2026 | Viewed by 82 | Submission Open

Keywords: fractional calculus; anomalous heat and mass transfer; renewable and hybrid energy systems; geothermal applications; viscoelastic modelling; computational strategies

(This special issue belongs to the Section Engineering)

Recent Advances in Fractional-Order Equations and Their Applications in Modern Energy Systems

edited by Zhe Gao, Xiaoting Gao and Enchang Cui

submission deadline 15 Jul 2026 | 2 articles | Viewed by 4138 | Submission Open

Keywords: fractional-order control theory in modern energy systems; theoretical frameworks and foundations of fractional-order equations in modern energy systems; fractional-order modeling and analysis of modern energy systems; fractional-order control systems and implementation of modern energy systems; applications of fractional-order equations in renewable energy sources; fractional-order control and optimization of energy systems; fractional-order dynamics in energy storage and energy conversion systems; case studies and implementations of fractional-order models in energy systems; energy storage systems; supercapacitors and batteries; and hybrid energy storage

(This special issue belongs to the Section Engineering)

Recent Developments in Multidimensional Fractional Differential Equations and Fractional Difference Equations

edited by

Marko Kostić

and

Wei-Shih Du

submission deadline 18 Jul 2026 | 3 articles | Viewed by 3340 | Submission Open

Keywords: fractional calculus; fractional differential equations; fractional difference equations; multidimensional fractional calculus; multidimensional fractional differential equations; multidimensional partial fractional differential equations; theory and applications

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

Chaotic and Fractal Approaches with AI for Multidisciplinary Modeling and Applications

edited by

Akif Akgül

and

Esteban Tlelo-Cuautle

submission deadline 20 Jul 2026 | Viewed by 71 | Submission Open

Keywords: chaos theory; fractals; artificial intelligence (AI); neural networks; hybrid AI approaches; chaotic neural networks; fractional calculus; engineering applications

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

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

edited by

Rodica Luca

submission deadline 20 Jul 2026 | Viewed by 37 | 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 Computational Methods for Fractal and Fractional Nonlinear Partial Differential Equations

edited by

Kang-Jia Wang

and

Inés Tejado

submission deadline 31 Jul 2026 | 4 articles | Viewed by 4133 | Submission Open

Keywords: fractal and fractional nonlinear partial differential equations; fractal and fractional calculus; mathematical physics; fractal variational principle

(This special issue belongs to the Section Mathematical Physics)

Advances in Dynamics and Control of Fractional-Order Systems

edited by Ruihong Li

submission deadline 31 Jul 2026 | 6 articles | Viewed by 3566 | Submission Open

Keywords: complex dynamical behaviors; bifurcation analysis; stability analysis; resonance analysis; chaos synchronization; control strategies; system identification

(This special issue belongs to the Section Engineering)

Implementations and Applications of Algorithms Based on Fractional Calculus to Engineering Problems

edited by

José de Jesús Rangel Magdaleno

and

Oscar Martínez-Fuentes

submission deadline 31 Jul 2026 | 2 articles | Viewed by 3555 | Submission Open

Keywords: fractional calculus; fractional-order systems; algorithm implementation; algorithm development; signal processing; image processing; fault detection

(This special issue belongs to the Section Engineering)

Applications of Fractal Analysis in Underground Engineering, Second Edition

edited by

,

,

,

, Defu Zhu and Kaijun Miao

submission deadline 31 Jul 2026 | 3 articles | Viewed by 1948 | Submission Open

Keywords: fractal analysis; fractal characteristics; data fractal processing; rock mechanics; rock engineering; under engineering; water/gas/heat conduction; joints; fractures and voids; fluid migration; chaos and roughness; image processing process; entropy

(This special issue belongs to the Section Engineering)

Applications of Fractal Interpolation in Mathematical Functions

edited by

Cristina Pacurar

and

Peter Massopust

submission deadline 31 Jul 2026 | 2 articles | Viewed by 982 | Submission Open

Keywords: fractal interpolation functions (FIFs); fractal functions and surfaces; iterated function systems (IFS); self-similarity and nonlinearity; self-affine and self-conformal structures; fractal approximation and modeling; function approximation; irregular and complex data modeling; signal and image processing; data fitting and curve reconstruction; mathematical and computational algorithms; applications in engineering; finance; biology; and natural sciences; multifractal analysis; function spaces and interpolation theory; fractal geometry in applied mathematics

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

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

edited by

Genly Leon

submission deadline 31 Jul 2026 | Viewed by 454 | 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 159 | 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)

Fractional Dynamics Systems: Modeling, Forecasting, and Control

edited by Seenith Sivasundaram,

Devaraj Vivek

and

Carlo Bianca

submission deadline 31 Jul 2026 | Viewed by 58 | Submission Open

Keywords: fractional-order systems; modeling and simulation; fractional-order control; stability and controllability; applications in engineering; biology; and finance; non-local dynamics

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

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 46 | 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 86 | 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 | 5 articles | Viewed by 5182 | 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 | 1 articles | Viewed by 1086 | 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)

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 243 | 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

Fractional-Order Dynamics in AI: Neural Networks and Applications

edited by

Eva H. Dulf

submission deadline 20 Aug 2026 | 1 articles | Viewed by 593 | 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 87 | 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 | 6 articles | Viewed by 6560 | 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)

Applications of Fractal Dimensions in Rock Mechanics and Geomechanics

edited by

Hai Pu

and Kangsheng Xue

submission deadline 31 Aug 2026 | 5 articles | Viewed by 4244 | 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 | 2 articles | Viewed by 1628 | 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)

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 775 | 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 | Viewed by 315 | 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

Fractal and Fractional Order Modeling of Real-World Phenomena

edited by

Stefan Balint

submission deadline 31 Aug 2026 | Viewed by 111 | 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 53 | 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 Syed Jawad Hussain Shahzad

submission deadline 9 Sep 2026 | Viewed by 103 | 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 2301 | Submission Open

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

(This special issue belongs to the Section Mathematical Physics)

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

edited by

Gabriel Bengochea

and

Manuel Duarte Ortigueira

submission deadline 15 Sep 2026 | 1 articles | Viewed by 551 | 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 1859 | 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 | 1 articles | Viewed by 1278 | 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 | 1 articles | Viewed by 492 | 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)

Calculus of Variations, Fractional Calculus and Their Applications

edited by

Matheus J. Lazo

submission deadline 30 Sep 2026 | Viewed by 359 | 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)

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 | Viewed by 281 | 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)

Fractal Approaches and Machine Learning in Financial Markets

edited by

Sun-Yong Choi

submission deadline 30 Sep 2026 | Viewed by 185 | Submission Open

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

Fractional Fourier Transform for Optical Signal and Image Processing

edited by

Pedro Chamorro-Posada

submission deadline 30 Sep 2026 | Viewed by 65 | 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 60 | 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)

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

edited by Zhiguo Luo and Danfeng Luo

submission deadline 30 Sep 2026 | Viewed by 51 | 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)

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 | Viewed by 51 | 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)

Applied Fractional Calculus in Machine Learning and Biomedical Engineering

edited by

Saptarshi Das

submission deadline 31 Oct 2026 | 2 articles | Viewed by 6322 | 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)

Fractal Functions: Theoretical Research and Application Analysis

edited by Yong-Shun Liang and Jia Liu

submission deadline 31 Oct 2026 | 5 articles | Viewed by 6230 | 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)

Advances in Fractal Analysis for Financial Risk Assessment

edited by

Valentin Radu

and

Catalin Dumitrescu

submission deadline 31 Oct 2026 | 2 articles | Viewed by 1164 | 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)

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 283 | 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)

Recent Advances in Fractal Analysis for Hydrocarbon Dynamics and Flow Modeling

edited by

Meng Wang

and

Weidong Xie

submission deadline 31 Oct 2026 | Viewed by 272 | 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 | Viewed by 147 | 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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