Fractal and Fractional

Recent Trends in Fractional Integral and Derivative Operators

edited by Arman Dabiri

submission deadline 10 Dec 2025 | Viewed by 243 | Submission Open

Keywords: time-delay systems; control theory for continuum systems; fractional-order systems; fractals and chaos; Volterra integro-differential systems; stochastic systems; diffusion and random walk processes; non-Markov processes; computational methods for nonlocal operators

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

Design, Optimization and Applications for Fractional Chaotic System

edited by

José Cruz Nunez-Perez

and

Vincent Ademola Adeyemi

submission deadline 15 Dec 2025 | 6 articles | Viewed by 13443 | Submission Open

Keywords: applications of chaotic systems and circuits; chaos; fractional-order circuits; fractional-order systems; fractional-order models; fractional-order mem-elements; hyperchaos; optimization; synchronization

(This special issue belongs to the Section Engineering)

Fractional Control Systems and Estimation: Control, State Observers and Parameter Estimation

edited by

Manuel A. Duarte-Mermoud

and

Gustavo Ceballos-Benavides

submission deadline 15 Dec 2025 | 5 articles | Viewed by 4914 | Submission Open

Keywords: adaptive identification and control; robust control; PID control; parameter estimation; state observers; Liouville– Caputo; Riemann– Liouville; Grunwald– Letnikov; adaptive systems and artificial intelligence

(This special issue belongs to the Section Engineering)

Advances in Fractional Order Systems and Robust Control, 2nd Edition

edited by

Feng Liu

submission deadline 20 Dec 2025 | 5 articles | Viewed by 9276 | Submission Open

Keywords: fractional order systems; fractional differential equations; robust control; fractional controllers; stability analysis; modeling

(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 25 Dec 2025 | 4 articles | Viewed by 3137 | 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)

Fractional Systems, Integrals and Derivatives: Theory and Application

edited by

Andrey Zahariev

and

Hristo Kiskinov

submission deadline 31 Dec 2025 | 17 articles | Viewed by 22545 | Submission Open

Keywords: fractional derivatives of constant order; distributed order fractional derivative; variable order fractional derivative; fractional differential equations/systems; functional-differential equations/systems; stability analysis of fractional-order systems

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

Fractional Calculus and Nonlinear Analysis: Theory and Applications

edited by

Wei-Shih Du

,

Marko Kostić

and

Daniel Velinov

submission deadline 31 Dec 2025 | 6 articles | Viewed by 12485 | 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)

Mathematical Inequalities in Fractional Calculus and Applications, 2nd Edition

edited by

Seth Kermausuor

and

Eze Nwaeze

submission deadline 31 Dec 2025 | 9 articles | Viewed by 9405 | Submission Open

Keywords: fractional calculus; caputo derivative; riemann-liouville derivative; discrete fractional calculus; fractals; fractional differential equations; mathematical inequalities; time scales

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

Analysis of Heat Conduction and Anomalous Diffusion in Fractional Calculus

edited by

Aloisi Somer

and

Ervin K. Lenzi

submission deadline 31 Dec 2025 | 7 articles | Viewed by 7343 | Submission Open

Keywords: fractional calculus and fractal media; thermo-molecular physics; thermodynamics; heat and mass transfer; bio-heat transfer; fractional thermal conduction; anomalous thermal diffusion; nonequilibrium processes; nonequilibrium thermodynamics; kinetics theory

(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 31 Dec 2025 | 8 articles | Viewed by 5910 | 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)

Fractal and Fractional Models in Soil Mechanics

edited by Yi Pik Helen Cheng and Luju Liang

submission deadline 31 Dec 2025 | 3 articles | Viewed by 4434 | Submission Open

Keywords: fractals and fragmentation; fractional-order mechanics; force network analysis; constitutive models; analytical and numerical methods; particle shape; macro- to micromechanical granular behavior; particle size effect; crushable soil mechanics; particle breakage and fragmentation; discrete element method

(This special issue belongs to the Section Engineering)

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

edited by

Zhouchao Wei

and Lulu Lu

submission deadline 31 Dec 2025 | 3 articles | Viewed by 4132 | 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 Fractal Dimensions in Rock Mechanics and Geomechanics

edited by

Hai Pu

and Kangsheng Xue

submission deadline 31 Dec 2025 | 5 articles | Viewed by 3866 | Submission Open

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

(This special issue belongs to the Section Engineering)

New Trends on Generalized Fractional Calculus, 2nd Edition

edited by

Milton Ferreira

,

Maria Manuela Fernandes Rodrigues

and

Nelson Felipe Loureiro Vieira

submission deadline 31 Dec 2025 | 2 articles | Viewed by 3190 | Submission Open

Keywords: generalised fractional calculus; fractional calculus with general analytic kernels; ψ -fractional derivatives; weighted fractional derivatives; integral transforms; special functions; fractional inequalities; fractional ODE and PDE; initial and Boundary value problems

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

Recent Trends in Computational Physics with Fractional Applications

edited by

Lanre Akinyemi

,

Mehmet Senol

,

Solomon Manukure

and Udoh Akpan

submission deadline 31 Dec 2025 | 5 articles | Viewed by 3137 | Submission Open

Keywords: stability analysis; integral equations; semi-analytical method; traveling wave solutions; analytical and numerical methods; soliton theory and its applications; fractional calculus and its applications; ordinary and partial differential equations; symmetry analysis and conservation laws; mathematical modeling of flow in porous media; multi-scale approaches to modeling wave phenomena; high-order numerical differential formulas for fractional derivatives; numerical and computational methods in fractional differential equations

(This special issue belongs to the Section Mathematical Physics)

Fractional Elliptic and Parabolic Equations: Analysis and Related Topics

edited by Wenxiong Chen and Leyun Wu

submission deadline 31 Dec 2025 | 2 articles | Viewed by 3072 | Submission Open

Keywords: fractional elliptic equations; fractional parabolic equations; fractional laplacian; non-local operators; variational method; multiplicity numerical analysis; applications of fractional equations; nonlinearity; symmetry; monotonicity; a priori estimate; existence; non-existence; uniqueness; classification; method of moving planes; sliding method; etc.

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

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

edited by

Hengfei Ding

, Changpin Li and Min Cai

submission deadline 31 Dec 2025 | 3 articles | Viewed by 2950 | 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)

Time-Fractal and Fractional Models in Physics and Engineering

edited by Kyungsik Kim

submission deadline 31 Dec 2025 | 5 articles | Viewed by 2843 | 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)

Nonlinear Fractional Differential Equation and Fixed-Point Theory, 2nd Edition

edited by

Mujahid Abbas

and

Talat Nazir

submission deadline 31 Dec 2025 | 3 articles | Viewed by 2208 | Submission Open

Keywords: fixed point theory and its applications; approximation theory and its applications; variational inequality and its applications; fractional differential equations; iterated function system; fractal theory; differential equations; finite difference equations; nonlinear analysis; dynamical system; nonlinear convex analysis

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

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

edited by Xiaoli Chen,

Dongfang Li

and Ting Gao

submission deadline 31 Dec 2025 | 2 articles | Viewed by 1738 | 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)

From Fractals to Fractional Calculus: Nonlinear Dynamics and Hybrid Complex Systems

edited by Katica (Stevanović) Hedrih

submission deadline 31 Dec 2025 | 3 articles | Viewed by 1662 | Submission Open

Keywords: fractals; nonlinear dynamics; fractional calculus; mathematical phenomenology; hybrid systems; complex structures; discrete and continuous dynamic systems

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

Applications of Fractional-Order Calculus in Robotics, 2nd Edition

edited by

Abhaya Pal Singh

and

Kishore Bingi

submission deadline 31 Dec 2025 | 1 articles | Viewed by 1436 | Submission Open

Keywords: fractional calculus; fractional control; fractional modeling; robotics; fractal manipulators

Recent Research in Fractional-Order Controllers and Their Applications

edited by

Carla M. A. Pinto

,

Cristina I. Muresan

and

Dana Copot

submission deadline 31 Dec 2025 | Viewed by 1139 | Submission Open

Keywords: fractional-order control; FOPID; fractional calculus; modelling; implementation; stability analysis; control design

Modelling and Analysis of Fractional Behaviours: Alternative Approaches and Characterization

edited by

Jocelyn Sabatier

submission deadline 31 Dec 2025 | Viewed by 310 | Submission Open

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

(This special issue belongs to the Section Engineering)

Advances in Fractional-Order Circuit Models: Theory and Applications

edited by

Chunhua Feng

submission deadline 31 Dec 2025 | Viewed by 186 | Submission Open

Keywords: fractional-order circuits; fractional-order models; fractional-order chaotic systems; fractional-order calculus; fractional-order oscillator

(This special issue belongs to the Section Complexity)

Fractal and Fractional in Geomaterials, 2nd Edition

edited by Yifei Sun

submission deadline 15 Jan 2026 | 2 articles | Viewed by 3964 | Submission Open

Keywords: fractal media; fractional mechanics; micro-to-macro. geomaterials; nonconventional approach

(This special issue belongs to the Section Engineering)

Applications of Fractional-Order Grey Models, 2nd Edition

edited by

Lifeng Wu

and Shuli Yan

submission deadline 15 Jan 2026 | 4 articles | Viewed by 3488 | Submission Open

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

(This special issue belongs to the Section Engineering)

Fractional Dynamics in Epidemic Models: Theoretical Approaches and Applications

edited by

Qura Tul Ain

and

Anwarud Din

submission deadline 15 Jan 2026 | 2 articles | Viewed by 2441 | Submission Open

Keywords: fractional calculus; fractional stochastic models; fractional dynamics; fractional-order epidemic models; epidemiological modeling; fractional models

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

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

edited by

Arman Oshnoei

and

Soroush Oshnoei

submission deadline 20 Jan 2026 | 2 articles | Viewed by 1975 | 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)

Analysis of Geological Pore Structure Based on Fractal Theory

edited by Wei Yang and

Mianmo Meng

submission deadline 20 Jan 2026 | 2 articles | Viewed by 1761 | 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)

Fractal Analysis in Biology and Medicine

edited by

Ivan Zaletel

submission deadline 30 Jan 2026 | 4 articles | Viewed by 6768 | Submission Open

Keywords: fractal analysis; fractal dimension; complexity; self-similarity; neuroscience; morphometry; cell and tissue analysis

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

Advances in Fractional-Order Chaotic and Complex Systems

edited by

Chunhua Wang

,

Fei Yu

and

Wei Yao

submission deadline 31 Jan 2026 | 8 articles | Viewed by 10322 | Submission Open

Keywords: fractional-order theory; fractional-order systems; complex systems; chaos; chaotic systems; chaos applications; non-linear systems; neural networks

(This special issue belongs to the Section Complexity)

Advances in Fractional Integral Inequalities: Theory and Applications

edited by

Armando Gallegos

and

Jorge E. Macías Díaz

submission deadline 31 Jan 2026 | 5 articles | Viewed by 3372 | Submission Open

Keywords: fractional integral inequalities; numerical integrations methods; operator theory; convex and concave functions

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

Theoretical Development and Application in Analytical and Numerical Methods for Fractional Differential Equations

edited by

Xinguang Zhang

,

Yonghong Wu

and

Chuanjun Chen

submission deadline 31 Jan 2026 | 2 articles | Viewed by 2251 | Submission Open

Keywords: fractional differential equations; boundary value problems; fractional integrals and derivatives; fractional Partial differential equations; fixed-point theory; fractional network

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

Fractional-Order Systems: Modeling and Control Applications in Engineering

edited by

Jianwen Zhou

and

Tianwei Zhang

submission deadline 31 Jan 2026 | 2 articles | Viewed by 1700 | Submission Open

Keywords: fractional-order differential or difference equations; fractional controlling theories; fractional-order systems; numerical methods; optimization techniques; complex networks; neural networks; applications in robotics and automation; applications in power and electrical systems; applications in mechanical systems; applications in biomedical engineering; applications in signal processing and communications

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

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

edited by

Wei Cai

,

Xianglong Su

and

Wojciech Sumelka

submission deadline 31 Jan 2026 | 1 articles | Viewed by 1056 | 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)

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 31 Jan 2026 | 1 articles | Viewed by 762 | 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 Applications for Signal Processing and Data Science

edited by

Héctor Vázquez-Leal

and

Manuel Duarte Ortigueira

submission deadline 15 Feb 2026 | 2 articles | Viewed by 8205 | 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

Control, Optimization, and Artificial Intelligence Methods Involving Fractals and Fractional Calculus

edited by

Jae Hoon Jeong

,

Duarte Valério

and

Sachin Sakthi Kuppusami Sakthivel

submission deadline 20 Feb 2026 | Viewed by 838 | Submission Open

Keywords: fractals; fractional calculus; control systems; optimization; artificial intelligence; machine learning; tracking; detection; segmentation; fractional-order models; fractal neural networks; evolutionary algorithms; signal processing; computer vision; autonomous systems

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

Harmonic and Geometric Analysis for Fractional Equations

edited by Leandro Tavares and

Alessio Fiscella

submission deadline 25 Feb 2026 | 2 articles | Viewed by 1891 | 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)

Fractional Integral Inequalities and Applications, 3rd Edition

edited by

Artion Kashuri

and

Hari Mohan Srivastava

submission deadline 28 Feb 2026 | 9 articles | Viewed by 9599 | Submission Open

Keywords: fractional integral inequalities; generalized convexity; numerical estimations; quantum calculus; multivariate analysis; means; operator theory; approximation theory

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

New Challenges Arising in Engineering Problems with Fractional and Integer Order, 4th Edition

edited by

Haci Mehmet Baskonus

,

Luis Manuel Sánchez Ruiz

and

Armando Ciancio

submission deadline 28 Feb 2026 | 7 articles | Viewed by 6490 | Submission Open

Keywords: new analytical and numerical methods to solve partial differential equations; computational methods for fractional differential equations; the analysis; modeling; and control of phenomena in the following areas; engineering problems; deterministic and stochastic fractional order models

(This special issue belongs to the Section Engineering)

Fractal Analysis and Its Applications in Rock Engineering, Second Edition

edited by

Xiaohan Yang

,

Lihai Tan

and Gaofeng Liu

submission deadline 28 Feb 2026 | 5 articles | Viewed by 4733 | Submission Open

Keywords: fractal analysis and modeling; fragmentation; rock mechanics; rock fractures; rock microstructures; rock engineering; geomechanical processes; engineering application

(This special issue belongs to the Section Engineering)

Advances in Fractional Initial and Boundary Value Problems

edited by

Sotiris K. Ntouyas

,

Bashir Ahmad

and

Jessada Tariboon

submission deadline 28 Feb 2026 | 4 articles | Viewed by 3166 | 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)

Fractal Mechanics of Engineering Materials, 2nd Edition

edited by

Mohd Nasir Tamin

and

Seyed R. Koloor

submission deadline 28 Feb 2026 | 2 articles | Viewed by 2976 | Submission Open

Keywords: fractal analysis; fractal dimension; fractal mechanics; continuum mechanics; fracture mechanics; fatigue and fatigue crack growth; damage mechanics; experimental mechanics

Advances in Fractional Modeling and Computation, Second Edition

edited by

,

,

and

submission deadline 28 Feb 2026 | 1 articles | Viewed by 1090 | Submission Open

Keywords: fractional models in natural sciences; fractional models in economics and engineering; numerical algorithms and discretization; fractional differential systems with control theory; fractional dynamic systems; analysis of fractional models; stochastic methods for fractional models; Monte Carlo methods; Markov chains and processes; stochastic modeling and simulation; related fractional models

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

Theoretical and Numerical Methods for Fractional and Nonlocal Partial Differential Equations

edited by

Giuseppe Di Fazio

and Giovanni Molica Bisci

submission deadline 28 Feb 2026 | 1 articles | Viewed by 479 | Submission Open

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

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

Multifractal Analysis and Complex Systems

edited by

Enrico De Santis

and Alessio Martino

submission deadline 28 Feb 2026 | Viewed by 241 | 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)

Stochastic Models, Fractional Calculus and Non-Local Operators: Theoretical Results and Applications

edited by Enrica Pirozzi, Luisa Beghin, Janusz Gajda and Lauri Viitasaari

submission deadline 1 Mar 2026 | 2 articles | Viewed by 1362 | Submission Open

Keywords: statistical analysis of fractional models; fractional Brownian motion; fractional diffusion processes; fractional stochastic differential equations

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

Fractal Applications in Thermal Engineering

edited by Qingyong Zhu

submission deadline 10 Mar 2026 | Viewed by 162 | Submission Open

(This special issue belongs to the Section Engineering)

Journal Menu

Journal Browser

Special Issues

Further Information

Guidelines

MDPI Initiatives

Follow MDPI