Fractal and Fractional

Numerical Solutions of Caputo-Type Fractional Differential Equations and Derivatives

edited by Phumlani Dlamini and Simphiwe Simelane

submission deadline 30 Sep 2025 | 15 articles | Viewed by 19058 | Submission Open

Keywords: Caputo-type fractional differential equations; Caputo-type fractional derivatives; generalized fractional derivatives; fractional inequalities; fractional operator; fractional Green’ s functions; fractional Laplace transform; fractional evolution equations; finite difference schemes; spectral methods; existence and uniqueness; stability; controllability; iterative learning controls

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

Variational Problems and Fractional Differential Equations

edited by Zhisu Liu and Yu Su

submission deadline 30 Sep 2025 | 9 articles | Viewed by 13145 | Submission Open

Keywords: variational problems; fractional differential equations; priori estimate; existence; non-existence; and uniqueness; regularity and symmetry; stability; asymptotic behavior

(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 2025 | 1 articles | Viewed by 957 | 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 Derivatives in Mathematical Modeling and Applications

edited by

Damian Słota

,

Rafal Brociek

and

Edyta Hetmaniok

submission deadline 30 Sep 2025 | 1 articles | Viewed by 802 | Submission Open

Keywords: fractional calculus; mathematical modeling; fractional differential equation; numerical methods; fractional integro-differential equations; optimization problems

(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 30 Sep 2025 | 1 articles | Viewed by 718 | 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)

Modeling, Optimization, and Control of Fractional-Order Neural Networks and Nonlinear Systems

edited by

Kaibo Shi

,

Zhinan Peng

, Xin Wang and

Xiao Cai

submission deadline 1 Oct 2025 | 13 articles | Viewed by 24395 | 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)

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

edited by

Yusuf Gürefe

submission deadline 1 Oct 2025 | 8 articles | Viewed by 6084 | 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)

Multifractals, Turbulence and Complexity in Geoscience and Space Science, 2nd Edition

edited by Mirko Stumpo,

Simone Benella

and

Tommaso Alberti

submission deadline 1 Oct 2025 | 1 articles | Viewed by 1075 | Submission Open

Keywords: fractals and multifractals; complexity and turbulence; extreme events; out of equilibrium; self-organization and criticality; multiplicative cascades and random multifractals; geoscience; space physics

(This special issue belongs to the Section Complexity)

Advances in Pattern Recognition—Image and Time Series Analyses—through Fractal Geometry and Complexity Theory

edited by Lucas C. Ribas, Leonardo F. S. Scabini and

Pier Luigi Gentili

submission deadline 31 Oct 2025 | 6 articles | Viewed by 13254 | Submission Open

Keywords: complex systems; pattern recognition; image processing; fractal descriptors; neural networks; network science

Fractional Calculus, Quantum Calculus and Special Functions in Complex Analysis

edited by

Gheorghe Oros

and

Georgia Irina Oros

submission deadline 31 Oct 2025 | 7 articles | Viewed by 8647 | Submission Open

Keywords: univalent functions; special functions; fractional operator; q– operator; differential subordination; differential superordination; quantum calculus

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

Flow and Transport in Fractal Models of Rock Mechanics

edited by Kouqi Liu

submission deadline 31 Oct 2025 | 4 articles | Viewed by 6734 | Submission Open

Keywords: fractal models; rock mechanics; transport process; oil and gas industry; reservoir characterization; numerical solution

(This special issue belongs to the Section Engineering)

Multiscale Fractal Analysis in Unconventional Reservoirs

edited by

Yang Wang

submission deadline 31 Oct 2025 | 10 articles | Viewed by 5659 | Submission Open

Keywords: multiscale fractal analysis; unconventional reservoirs; fractal geometry; fracture network characterization; pore structure analysis; fluid flow modeling; reservoir simulation; machine learning; digital rock physics

(This special issue belongs to the Section Engineering)

Applied Fractional Calculus in Machine Learning and Biomedical Engineering

edited by

Saptarshi Das

submission deadline 31 Oct 2025 | 2 articles | Viewed by 3829 | 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)

Advances in Nonlinear Functional Analysis on Fractional Differential Equations, 2nd Edition

edited by

Bipan Hazarika

submission deadline 31 Oct 2025 | 2 articles | Viewed by 2087 | Submission Open

Keywords: nonlinear functional analysis; control theory and applications; nonlinear fractional dynamic equations on timescale; fixed point theory; ecological systems; nonlinear dynamical systems; fractional calculus; solvability of infinite systems; sequence spaces and function spaces; nonlinear functionals and variational methods; nonlinear operators

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

Fractional Dynamics and Control in Multi-Agent Systems and Networks

edited by Huaiqin Wu and

Cheng Hu

submission deadline 31 Oct 2025 | 1 articles | Viewed by 749 | Submission Open

Keywords: system model; fractional-order dynamics; MASs and CNs; stability analysis; nonlinear control

(This special issue belongs to the Section Engineering)

Fractional Calculus Applied in Environmental Biosystems

edited by Diogo Francisco Rossoni and Gustavo de Souza Matias

submission deadline 31 Oct 2025 | Viewed by 650 | Submission Open

Keywords: bioprocess modeling; environmental models; biosystem anomalies; fractional calculus

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 2025 | Viewed by 201 | 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)

Mathematical and Numerical Analysis of Fractional Evolution Equations and Applications

edited by

Naben Parumasur

,

Vijay Kumar Kukreja

and

Pravin Singh

submission deadline 1 Nov 2025 | 1 articles | Viewed by 732 | 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)

Analysis and Modeling of Fractional-Order Dynamical Networks

edited by Wang Fei and

Feifei Du

submission deadline 14 Nov 2025 | 6 articles | Viewed by 7633 | Submission Open

Keywords: fractional-order systems; neural networks; gene regulatory networks; dynamical networks; multi-agent systems; coupled systems; synchronization control; heterogeneous networks; analysis of dynamic behavior

(This special issue belongs to the Section Complexity)

Recent Advances in the Spatial and Temporal Discretizations of Fractional PDEs, Second Edition

edited by

Xian-Ming Gu

, Hongbin Chen and

Xiangcheng Zheng

submission deadline 14 Nov 2025 | 6 articles | Viewed by 3342 | Submission Open

Keywords: fractional PDEs; finite difference; finite element; finite volume; spectral methods; nonuniform and adaptive discretizations; adaptive space– time methods; parallel-in-time methods; numerical methods; numerical treatments of integro-differential equations; nonlocal modeling and computation; convolution quadratures; modeling and simulations

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

Women’s Special Issue Series: Fractal and Fractional, 2nd Edition

edited by

Ivanka Stamova

and

Dana Copot

submission deadline 15 Nov 2025 | 4 articles | Viewed by 6822 | Submission Open

Keywords: fractals and fractional calculus; fractals and fractional calculus in computing; fractals and fractional calculus in mathematical physics; fractals and fractional calculus in biology and neurocomputing; fractals and fractional calculus in engineering; fractals and fractional calculus in economics; fratals and fractional calculus in educational technologies; fractional calculus and control; fractional calculus and optimization; fractional calculus and stability; fractional models and uncertainty; related fractional modeling

(This special issue belongs to the Section Complexity)

AI-Driven Fractal Models for Complex Systems

edited by

Dong Hao

and

María A. Navascués

submission deadline 22 Nov 2025 | Viewed by 332 | Submission Open

Keywords: fractal model and AI for social network and human behaviour; fractal AI models in economic and finance; AI-based fractal models for LLMS and NLP systems; intersection of fractal models and machine learning

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

Recent Advances in Fractional Fourier Transforms and Applications, 2nd Edition

edited by

Zunwei Fu

,

Bingzhao Li

and

Xiangyang Lu

submission deadline 25 Nov 2025 | 6 articles | Viewed by 6735 | Submission Open

Keywords: fractional Fourier transform; linear canonical transform; digital signal processing; fractional integral operator; partial differential equations

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

Fractal Analysis and Fractal Dimension in Materials Chemistry, 2nd Edition

edited by

Gianina Dobrescu

,

Florica Papa

and

Razvan State

submission deadline 25 Nov 2025 | 1 articles | Viewed by 1633 | Submission Open

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

Fractional Processes and Systems in Computer Science and Engineering

edited by

Ming Li

and

Junyu He

submission deadline 30 Nov 2025 | 8 articles | Viewed by 8970 | Submission Open

Keywords: fractional processes; fractional systems; fractal dimensions; fractal time series; long-range dependence; fractal paths; anomalous diffusion behavior; stochastic processes; fractional Brownian motion; fractional derivative; fractional Gaussian noise; fractional models

(This special issue belongs to the Section Engineering)

Advances in Boundary Value Problems for Fractional Differential Equations, 3rd Edition

edited by

Rodica Luca

submission deadline 30 Nov 2025 | 13 articles | Viewed by 8964 | 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)

Fractals in Biophysics and Their Applications

edited by Anirban Bandyopadhyay

submission deadline 30 Nov 2025 | 5 articles | Viewed by 8174 | Submission Open

Keywords: quantum mechanics; quantum biology; biophysics; biophotonics; bioelectronics; neuroscience; brain dynamics; fractal analysis in medicine; water network in biology

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

Fractional-Order Dynamics and Control in Green Energy Systems

edited by Manashita Borah and

Christos Volos

submission deadline 30 Nov 2025 | 5 articles | Viewed by 7933 | Submission Open

Keywords: fractional-order chaos; energy storage systems; dynamics; control systems; energy storage systems; biological systems; renewable energy applications; energy-efficient robots; green transportation

(This special issue belongs to the Section Engineering)

Recent Trends in Fractional Integral and Derivative Operators

edited by Arman Dabiri

submission deadline 10 Dec 2025 | Viewed by 138 | 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 11828 | 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 | 3 articles | Viewed by 2859 | 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 | 4 articles | Viewed by 7518 | 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 | 2 articles | Viewed by 1074 | 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 | 15 articles | Viewed by 18175 | 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 11241 | 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 | 8 articles | Viewed by 7054 | 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 | 6 articles | Viewed by 5527 | 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 | 5 articles | Viewed by 3550 | 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)

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 3255 | 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)

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 3097 | 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)

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 2638 | 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)

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 2597 | 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)

Applications of Fractal Dimensions in Rock Mechanics and Geomechanics

edited by

Hai Pu

and Kangsheng Xue

submission deadline 31 Dec 2025 | 3 articles | Viewed by 1826 | Submission Open

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

(This special issue belongs to the Section Engineering)

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 1807 | 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)

Recent Trends in Computational Physics with Fractional Applications

edited by

Lanre Akinyemi

,

Mehmet Senol

,

Solomon Manukure

and Udoh Akpan

submission deadline 31 Dec 2025 | 3 articles | Viewed by 1797 | 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)

Modeling and Dynamic Analysis of Fractional-Order Systems

edited by Li Ma and Fanhai Zeng

submission deadline 31 Dec 2025 | 3 articles | Viewed by 1600 | Submission Open

Keywords: stability and control of fractional-order systems; reductions for fractional-order systems; bifurcation and chaos in fractional-order systems; discrete-time or continuous-time fractional-order systems; modeling via fractional calculus; generalized fractional calculus; numerical methods for fractional-order systems

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

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 976 | Submission Open

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

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

edited by

Mujahid Abbas

and

Talat Nazir

submission deadline 31 Dec 2025 | 2 articles | Viewed by 785 | 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 | 1 articles | Viewed by 692 | 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 | 1 articles | Viewed by 573 | 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)

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