Fractal and Fractional

Numerical Solution and Applications of Fractional Differential Equations, 3rd Edition

edited by

Libo Feng

,

Yang Liu

and

Lin Liu

submission deadline 10 Jul 2026 | 9 articles | Viewed by 9970 | Submission Open

Keywords: numerical methods; mathematical modelling; fractional calculus; fractional differential equations; numerical analysis; fast algorithm

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

Recent Advances in Fractional-Order Neural Networks: Theory and Application, 2nd Edition

edited by

Zhouchao Wei

and Lulu Lu

submission deadline 10 Jul 2026 | 3 articles | Viewed by 5508 | Submission Open

Keywords: fractional calculus; dynamics analysis; biological nervous system; circuit design and simulation; artificial intelligence

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

Applications of Fractional-Order Grey Models, 2nd Edition

edited by

Lifeng Wu

and Shuli Yan

submission deadline 15 Jul 2026 | 6 articles | Viewed by 8332 | Submission Open

Keywords: fractional-order; grey model; prediction; algorithm; application

(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 5288 | 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 | 5 articles | Viewed by 6597 | 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 | 1 articles | Viewed by 1438 | 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)

Fractional Calculus and Nonlinear Analysis: Theory and Applications

edited by

Wei-Shih Du

,

Marko Kostić

and

Daniel Velinov

submission deadline 31 Jul 2026 | 8 articles | Viewed by 15732 | Submission Open

Keywords: fractional differential equation; fractional complicated system; fractional operator; modeling biological phenomena; nonlinear dynamics and chaos; fixed point theory; optimization; critical point theory; optimization; convex analysis

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

Advances in Dynamics and Control of Fractional-Order Systems

edited by Ruihong Li

submission deadline 31 Jul 2026 | 15 articles | Viewed by 11230 | 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)

Analysis of Geological Pore Structure Based on Fractal Theory

edited by Wei Yang and

Mianmo Meng

submission deadline 31 Jul 2026 | 9 articles | Viewed by 7919 | Submission Open

Keywords: fractal theory; fractal analysis; multifractal theory; multifractal analysis; pore structure; pore–crack observation; pore connectivity

(This special issue belongs to the Section Engineering)

Recent Computational Methods for Fractal and Fractional Nonlinear Partial Differential Equations

edited by

Kang-Jia Wang

and

Inés Tejado

submission deadline 31 Jul 2026 | 6 articles | Viewed by 7520 | 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)

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 | 3 articles | Viewed by 5465 | 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 | 5 articles | Viewed by 4917 | 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)

Recent Advances in Fractional Differential Equations and Their Applications, 3rd Edition

edited by Xiaoli Chen,

Dongfang Li

and Ting Gao

submission deadline 31 Jul 2026 | 3 articles | Viewed by 3455 | Submission Open

Keywords: nonlocal differential equations; fractional differential equations; stochastic differential equations; numerical method; machine learning methods

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

Applications of Fractal Interpolation in Mathematical Functions

edited by

Cristina Pacurar

and

Peter Massopust

submission deadline 31 Jul 2026 | 3 articles | Viewed by 2474 | 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)

Fractal Analysis and Data-Driven Complex Systems

edited by

J. Alberto Conejero

submission deadline 31 Jul 2026 | 4 articles | Viewed by 2326 | Submission Open

Keywords: fractal geometry; multifractal analysis; fractional brownian motion; time-series analysis; scaling laws and self-similarity

(This special issue belongs to the Section Complexity)

Fractional Dynamics Systems: Modeling, Forecasting, and Control

edited by Seenith Sivasundaram,

Devaraj Vivek

and

Carlo Bianca

submission deadline 31 Jul 2026 | 2 articles | Viewed by 1580 | 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)

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 657 | 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 435 | 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 265 | 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 272 | 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 7445 | 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 2472 | 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 2165 | 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 484 | 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 | 8 articles | Viewed by 6887 | 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 1600 | 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 287 | 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 | 10 articles | Viewed by 18346 | 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 | 10 articles | Viewed by 9867 | 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 | 8 articles | Viewed by 9105 | 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 4737 | 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 2559 | Submission Open

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

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

edited by Leunglung Chan

submission deadline 31 Aug 2026 | 2 articles | Viewed by 1744 | 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)

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 | 2 articles | Viewed by 1719 | 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 1693 | 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 | 1 articles | Viewed by 771 | 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 | 1 articles | Viewed by 388 | 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 1504 | 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 3579 | 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 3117 | 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 2723 | 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 2294 | 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 | 3 articles | Viewed by 1891 | 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 | 3 articles | Viewed by 3399 | 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 2430 | 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)

Fractal Approaches and Machine Learning in Financial Markets

edited by

Sun-Yong Choi

submission deadline 30 Sep 2026 | 4 articles | Viewed by 2198 | Submission Open

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

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 1959 | 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)

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 1444 | 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)

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 1146 | 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)

Calculus of Variations, Fractional Calculus and Their Applications

edited by

Matheus J. Lazo

submission deadline 30 Sep 2026 | 1 articles | Viewed by 1075 | 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)

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