Fractal and Fractional

Numerical Analysis and Iterative Methods for Fractional Differential Equations

edited by

and

submission deadline 13 Jun 2026 | 5 articles | Viewed by 4244 | Submission Open

Keywords: fractional differential equations; fractional-order differential equations; nonlinear fractional equations; fuzzy fractional differential equations; numerical methods and computational techniques; stability and consistency; local and global convergence; iterative methods; dynamical behaviors; topological methods; hybrid block methods; comparative analysis; error analysis and adaptive methods; applications of fractional differential equations in systems and signal processing; applications of nonlinear fractional equations in physics; biology; and engineering

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

Pore Structure and Fractal Characteristics in Unconventional Oil and Gas Reservoirs, 2nd Edition

edited by

Zine El Abiddine Fellah

, Jizhen Zhang and

Quanzhong Guan

submission deadline 15 Jun 2026 | 11 articles | Viewed by 10357 | Submission Open

Keywords: pore structure; pore heterogeneity; complexity; fractal characteristics; microstructures; fractal cracks

(This special issue belongs to the Section Engineering)

Time-Fractal and Fractional Models in Physics and Engineering

edited by Kyungsik Kim

submission deadline 15 Jun 2026 | 7 articles | Viewed by 6675 | Submission Open

Keywords: fractals; multifractals; MDFA; MDCCA; fractional analysis; thermodynamics; statistical mechanics; machine learning; artificial intelligence; complex network; image recognition; fluid climate and global change; econophysics; brain network

(This special issue belongs to the Section Complexity)

Exploration and Analysis of Higher-Order Numerical Methods for Fractional Differential Equations

edited by

Hengfei Ding

, Changpin Li and Min Cai

submission deadline 15 Jun 2026 | 4 articles | Viewed by 4831 | Submission Open

Keywords: the modeling of fractional differential equations; finite difference methods for fractional differential equations; finite element methods for fractional differential equations; spectral methods for fractional differential equations; the construction of higher-order numerical differential formulas for fractional derivatives

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

Fractional Mathematical Modelling: Theory, Methods, and Applications—2nd Edition

edited by

Zeeshan Ali

and

Sandra Pinelas

submission deadline 16 Jun 2026 | 3 articles | Viewed by 2887 | Submission Open

Keywords: fractional mathematical modeling; fractional differential and integral equations; novel fractional-order operators and their properties; existence and uniqueness of solutions; analytical techniques for fractional systems; numerical methods and computational algorithms; stability and control of fractional-order systems; real-world applications across science and engineering; integration with machine learning; stochastic analysis; and hybrid modeling; interdisciplinary modeling of complex systems

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

Fractional Order Complex Systems: Advanced Control, Intelligent Estimation and Reinforcement Learning Image Processing Algorithms, Second Edition

edited by

Jin-Xi Zhang

,

Xuefeng Zhang

, Driss Boutat and

Da-Yan Liu

submission deadline 25 Jun 2026 | 12 articles | Viewed by 17136 | Submission Open

Keywords: image processing; image fusion; image denoising; stability of fractional systems; control of fractional systems; singular fractional systems

(This special issue belongs to the Section Engineering)

Numerical and Exact Methods for Nonlinear Differential Equations and Applications in Physics, 2nd Edition

edited by

Yusuf Gürefe

submission deadline 30 Jun 2026 | 10 articles | Viewed by 14112 | Submission Open

Keywords: fractional calculus; special functions in fractional calculus; mathematical modelling in physics; nonlinear models in mathematical physics; dynamics of physical systems; numerical solutions; exact solutions; soliton theory; computational physics; multiplicative calculus; fuzzy differential calculus; stochastic differential equations

(This special issue belongs to the Section Mathematical Physics)

Applications of Fractional Calculus in Modern Mathematical Modeling

edited by

Feliz Manuel Minhós

,

Ali Raza

and

Muhammad Mohsin

submission deadline 30 Jun 2026 | 8 articles | Viewed by 10490 | Submission Open

Keywords: fractional calculus; fractional differential equations (FDEs); fractional delay differential equations (FDDEs); stochastic fractional delay differential equations (SFDDEs); memory effects; fractional partial differential equations (FRDE's); stochastic fractional partial differential equations (SFPDEs); existence and uniqueness of solutions for FDEs; stability analysis of FDEs; sufficient conditions for solvability of FDEs with multi-point type data; uniqueness of solution for FDEs with impulses given by functions with several variables; solvability of functional FDES in involving P-Laplacian; multiplicity results for singular FDES in biological models; numerical methods in fractional calculus; biological systems modeling through fractional calculus; efficient computational methods to solve fractional differential equations for biological systems; control theory; mathematical modeling in finance through fractional calculus; data-driven approaches through fractional calculus; machine learning with fractional operators; future research directions and open problems in the application of fractional calculus in mathematical modeling

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

Fractional Order Systems with Application to Electrical Power Engineering, 3rd Edition

edited by

Arman Oshnoei

and

Soroush Oshnoei

submission deadline 30 Jun 2026 | 8 articles | Viewed by 7879 | 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)

Fractional Gravity/Cosmology in Classical and Quantum Regimes, Second Edition

edited by

Seyed Meraj Mousavi Rasouli

and

Shahram Jalalzadeh

submission deadline 30 Jun 2026 | 2 articles | Viewed by 7390 | Submission Open

Keywords: fractional calculus; fractional derivatives; riesz fractional operator; caputo fractional operator; fractional Brownian motion; levy path integrals; fractional-action-like variational approach; fractional quantum mechanics; fractional classical cosmology; fractional quantum cosmology; non-local operators

(This special issue belongs to the Section Mathematical Physics)

Fractals in Earthquake and Atmospheric Science

edited by

Dimitrios Nikolopoulos

submission deadline 30 Jun 2026 | 6 articles | Viewed by 5438 | Submission Open

Keywords: fractals; self-organised systems; non-linear dynamics and chaos; radon; electromagnetism; geodesy; urban air pollution; earthquakes; modelling and simulation; data analysis: algorithms and implementation

(This special issue belongs to the Section Mathematical Physics)

Multi-Scale and Fractal Research on Advanced Manufacturing and Tribology

edited by

Feng Feng

and

Qiang Li

submission deadline 30 Jun 2026 | 3 articles | Viewed by 3768 | Submission Open

Keywords: manufacturing; rough surfaces; fractal method; multi-scale approach; tribology; contact mechanics; wear; friction; lubrication

(This special issue belongs to the Section Engineering)

Mathematical and Numerical Analysis of Fractional Evolution Equations and Applications

edited by

Naben Parumasur

,

Vijay Kumar Kukreja

and

Pravin Singh

submission deadline 30 Jun 2026 | 3 articles | Viewed by 3255 | Submission Open

Keywords: fractional PDEs; numerical solutions; exact solutions; fractional Sobolev spaces; distributed parameter systems; solitary and travelling waves

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

Fractional Calculus in the Design, Control and Implementation of Complex Systems, 2nd Edition

edited by

Ernesto Zambrano-Serrano

and

Miguel A. Platas-Garza

submission deadline 30 Jun 2026 | 1 articles | Viewed by 2848 | Submission Open

Keywords: fractional calculus; chaotic systems; complex networks; variable order calculus; mathematical modeling; control theory; complexity; circuit implementation; chaos-based cryptography; neural networks; identification and modeling; signal processing; complexity measures; chaos theory; applied mathematics

(This special issue belongs to the Section Complexity)

Applications of Fractal Analysis in Structural Geology

edited by

Jing Ba

, Yuhang Guo and

Cong Luo

submission deadline 30 Jun 2026 | 2 articles | Viewed by 2081 | Submission Open

Keywords: fractal geometry; structural complexity; scale invariance; fracture network modeling; seismic attribute analysis; reservoir heterogeneity; rock physics/seismic modeling; rock physics/seismic inversion; geomechanical prediction; digital geology; multiscale characterization; planetary geomorphology

(This special issue belongs to the Section Engineering)

New Horizons in Fractional and Fractal Dynamics: Unraveling Complexity in Chaotic Systems

edited by

Song Zheng

and

Liguo Yuan

submission deadline 30 Jun 2026 | 2 articles | Viewed by 1939 | Submission Open

Keywords: fractional-order systems; stability analysis; fractional-order control theory; high-dimensional fractional-fractal simulation; chaotic time series analysis; machine learning for fractional chaos; fractal network dynamics; biological oscillator modeling; economic fractal models; security encryption applications

(This special issue belongs to the Section Complexity)

Advances in Fractional-Order Control and Optimization for Sustainable Energy Systems

edited by

Jiuwu Hui

and

Aldo Jonathan Muñoz-Vazquez

submission deadline 30 Jun 2026 | 1 articles | Viewed by 1685 | Submission Open

Keywords: fractional-order control; fractional calculus; robust control; adaptive control; nonlinear systems; stability analysis; real-time applications

(This special issue belongs to the Section Engineering)

Fractional Stochastic Process: Theory and Applications

edited by

Wanqing Song

and

Francesco Villecco

submission deadline 30 Jun 2026 | 1 articles | Viewed by 1648 | Submission Open

Keywords: classic and quantum mechanics; equilibrium and non-equilibrium; fluids; granular and soft matter; fractional calculus in statistical mechanics; fractional calculus in statistical physics; interdisciplinary statistical mechanics; interdisciplinary statistical physics; fault diagnosis; life prediction; signals processing; neuronal signal analysis (EEG; BCI); mathematical modeling of diseases

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

Fractional Differential Operators with Classical and New Memory Kernels, Second Edition

edited by

Dimiter Prodanov

and

Jordan Hristov

submission deadline 30 Jun 2026 | 1 articles | Viewed by 1431 | Submission Open

Keywords: fractional operators; memory kernels; biomechanical and medical models; heat and mass transfer; analysis; special functions; and kernels; numerical and computational methods; analytical solution methods: exact and approximate; modeling approaches with nonlocal (fractional) operators; probability and statistics based on nonlocal approaches; mathematical physics: heat; mass; and momentum transfer; engineering applications and image processing; life science; biophysics; and complexity

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

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 | 1 articles | Viewed by 1334 | 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)

Advances in Fractional-Order PID Control: Theory and Applications

edited by

Jorge Mario Cruz-Duarte

and César-Fernando Méndez-Barrios

submission deadline 30 Jun 2026 | Viewed by 549 | 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 398 | 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 342 | Submission Open

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

(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 259 | 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)

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 9254 | 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 5328 | 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 | 5 articles | Viewed by 7605 | 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 5141 | 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)

Modelling and Analysis of Fractional Behaviours: Alternative Approaches and Characterization

edited by

Jocelyn Sabatier

submission deadline 15 Jul 2026 | Viewed by 507 | Submission Open

Keywords: fractional behaviours; modelling; non-singular kernels; fractal

(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 6055 | 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 1264 | 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 | 7 articles | Viewed by 15035 | 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 10031 | 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 | 8 articles | Viewed by 7002 | 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 6661 | 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 5073 | 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 4494 | 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 3278 | 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 2299 | 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 | 3 articles | Viewed by 1631 | 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 1253 | 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 626 | 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 360 | 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 228 | 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 228 | 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 7154 | 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 2122 | 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 1935 | 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 409 | 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 6054 | 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)

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