Fractal and Fractional

Boundary Value Problems for Nonlinear Fractional Differential Equations: Theory, Methods and Application

edited by

submission deadline 31 Mar 2025 | 10 articles | Viewed by 11486 | Submission Open

Keywords: existence and positivity of solutions; uniqueness and multiplicity of solutions; stability and equilibrium; fixed point methods and applications; modeling with FDEs; numerical solutions; neural networks and FDEs; eigenvalue problems; fractional q-differential equations

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

Fractional- and Integer-Order System: Control Theory and Applications, 2nd Edition

edited by

Thach Ngoc Dinh

,

Shyam Kamal

,

Rajesh Kumar Pandey

, Bijnan Bandyopadhyay and

Jun Huang

submission deadline 31 Mar 2025 | 4 articles | Viewed by 5488 | Submission Open

(This special issue belongs to the Section Engineering)

Biocomplexity and Fractal Analysis: Theory and Applications

edited by

Annamaria Zaia

and

Pierluigi Maponi

submission deadline 31 Mar 2025 | 1 articles | Viewed by 1916 | Submission Open

Keywords: biocomplexity; fractal analysis; biomathematical modeling; computer-aided diagnosis; biomarker; computational tools; biomedical imaging

(This special issue belongs to the Section Complexity)

New Advances and Applications of Fractional Oscillate System

edited by Liang Wang

submission deadline 31 Mar 2025 | 1 articles | Viewed by 1290 | Submission Open

Keywords: fractional calculus; fractional-order oscillate systems; stochastic dynamical systems; vibro-impact system; stochastic bifurcation and chaos

(This special issue belongs to the Section Engineering)

Fractional-Order Dynamics and Control in Green Energy Systems

edited by Manashita Borah and

Christos Volos

submission deadline 18 Apr 2025 | 3 articles | Viewed by 4583 | 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)

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

edited by

Rodica Luca

submission deadline 20 Apr 2025 | 4 articles | Viewed by 2492 | 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)

Applications of Fractals and Fractional Calculus in Nuclear Reactors

edited by Gilberto Espinosa Paredes

submission deadline 25 Apr 2025 | Viewed by 228 | Submission Open

Keywords: Nuclear Reactor analysis; fractal mathematical modeling; fractional mathematical modeling; fractional compartmental models; Mittag-Leffler kernel; stability analysis; semi-analytical method; analytical and numerical methods; symmetry analysis and conservation laws; numerical and computational methods

(This special issue belongs to the Section Mathematical Physics)

Fractional Differential Operators with Classical and New Memory Kernels

edited by

Dimiter Prodanov

and

Jordan Hristov

submission deadline 30 Apr 2025 | 13 articles | Viewed by 14222 | Submission Open

Keywords: fractional operators; memory kernels; biomechanical and medical models; 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 non-local 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)

Fractional-Order Controllers in Electronics and Automation Engineering

edited by

Allan G. Soriano-Sánchez

and Didier López-Mancilla

submission deadline 30 Apr 2025 | 3 articles | Viewed by 5726 | 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)

Advanced Numerical Methods for Fractional Functional Models

edited by

Kamyar Hosseini

,

Khadijeh Sadri

,

Evren Hınçal

,

Soheil Salahshour

and Farzaneh Alizadeh

submission deadline 30 Apr 2025 | 2 articles | Viewed by 2037 | Submission Open

Keywords: numerical methods; approximation methods; fractional differential equations; fractional partial differential equations; fractional integral equations; fractional functional models

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

Fractal Analysis and Its Applications in Materials Science

edited by

Zine El Abiddine Fellah

submission deadline 30 Apr 2025 | 1 articles | Viewed by 1110 | Submission Open

Keywords: fractal analysis; fractal materials; fractals media; metamaterial characterization; acoustic characterization; porous materials; micropolar materials; poroelastic /elastic materials; solid and fluid mechanics; self-similar media; fractal analysis and applications in materials science

(This special issue belongs to the Section Engineering)

Enhancing Pain Assessment and Anesthesia Management: Fractional Modeling with AI

edited by

Martine Neckebroek

submission deadline 30 Apr 2025 | 1 articles | Viewed by 1097 | Submission Open

Keywords: anesthesia and fractional calculus and AI; pain and fractional calculus and AI; neuro monitoring; fractional calculus

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

Applications of Fractal Analysis in Underground Engineering

edited by

Shihao Tu

, Lei Zhang,

Chen Wang

,

Cun Zhang

, Defu Zhu and Kaijun Miao

submission deadline 1 May 2025 | 11 articles | Viewed by 14569 | Submission Open

(This special issue belongs to the Section Engineering)

Fractals in Geology and Geochemistry

edited by

Fan Xiao

, Qiuming Cheng and Frits Agterberg

submission deadline 1 May 2025 | 7 articles | Viewed by 12196 | Submission Open

(This special issue belongs to the Section Engineering)

Fractal and Multifractal Analyses in Financial Markets and Economics, 2nd Edition

edited by

Jae Wook Song

submission deadline 1 May 2025 | 5 articles | Viewed by 6866 | Submission Open

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

Fractional Mathematical Modelling: Theory, Methods and Applications

edited by Faranak Rabiei,

Dongwook Kim

and

Zeeshan Ali

submission deadline 15 May 2025 | 8 articles | Viewed by 14120 | Submission Open

Keywords: fractional differential and integral equations; new fractional operators and their properties; existence and uniqueness of solutions; analytical and numerical methods; stability analysis; fractional calculus in physics; fractional dynamics in complex systems; applications to science and engineering

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

Application of Anomalous Diffusion Modeling Based on Fractal and Fractional Derivatives

edited by

Minghua Chen

, Jianxiong Cao,

An Chen

and

Hossein Jafari

submission deadline 15 May 2025 | 4 articles | Viewed by 5428 | Submission Open

Keywords: anomalous diffusion process; non-ergodic fractional dynamical systems; nonlocal and fractional models; fractional biology model; non-Gaussian noises; fractional stochastic differential equations; integral equations; finite difference methods; finite element methods; mathematical models for COVID-19; spectral methods; fractional lie symmetry; local fractional derivative

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

Fractal Mechanics of Engineering Materials, 2nd Edition

edited by

Mohd Nasir Tamin

and

Seyed R. Koloor

submission deadline 15 May 2025 | 1 articles | Viewed by 1230 | Submission Open

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

Distributed Control and Optimization of Fractional-Order Systems: Theory and Applications

edited by Jun Shen and Cuihong Wang

submission deadline 16 May 2025 | 1 articles | Viewed by 1136 | Submission Open

Keywords: fractional-order systems; fractional-order nonlinear systems; control theory and control engineering; optimal control; distributed control; multi-agent systems; cyber-physical systems; stability of dynamic systems

(This special issue belongs to the Section Engineering)

Application of Fractals in Complex Networks of Engineering and Medicine

edited by

Matej Babič

and

Andrej Srakar

submission deadline 21 May 2025 | 5 articles | Viewed by 12361 | Submission Open

Keywords: fractals; complex networks; data mining; complex systems; chaos; engineering; medicine

(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 25 May 2025 | 2 articles | Viewed by 1898 | 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)

Fractional Diffusion, Multistability and Control in Complex Systems

edited by Mingshu Peng

submission deadline 30 May 2025 | 4 articles | Viewed by 5700 | Submission Open

Keywords: turing instability; multistability; bifurcation; chaos; fractal differential equations; complexity; mathematical modelling; control; critical point theory; boundary value problem; stability; delay; diffusion; pattern formation; spatio-temporal behavior; related practical problem

(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 30 May 2025 | 3 articles | Viewed by 2542 | 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)

Pore Structure and Fractal Characteristics in Unconventional Oil and Gas Reservoirs

edited by

Zine El Abiddine Fellah

, Jizhen Zhang and Quanzhong Guan

submission deadline 31 May 2025 | 13 articles | Viewed by 15803 | Submission Open

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

(This special issue belongs to the Section Complexity)

Fixed Point Theory and Fractals

edited by

María A. Navascués

,

Bilel Selmi

and

Cristina Serpa

submission deadline 31 May 2025 | 5 articles | Viewed by 4257 | Submission Open

Keywords: fixed point theorems; fractal sets; functions and measures; fixed-point approximation and stability; iterative methods for the solution of differential and integral equations; iterated function systems; discrete dynamical systems; fractional calculus related to fixed point theory; dynamical systems or deterministic/stochastic fractals; applications of these fields

(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 May 2025 | 5 articles | Viewed by 4013 | 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)

Advanced Modeling and Methods of Statistical Processing of Stochastic Signals in Fractional Dynamic Systems

edited by

Serhii Lupenko

and Jacek Leśkow

submission deadline 13 Jun 2025 | 4 articles | Viewed by 7741 | Submission Open

Keywords: fractional stochastic processes; cyclostationary random processes; fractional-order signal processing; fractional and hybrid dynamic systems; signal statistical processing techniques; fractional-order machine learning techniques in signal processing; signal computer simulation techniques

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

Numerical Analysis and Iterative Methods for Fractional Differential Equations

edited by Mudassir Shams and

Bruno Carpentieri

submission deadline 13 Jun 2025 | Viewed by 378 | 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)

Applications of General Fractional Calculus Models: Insights into Viscoelasticity and Wave Propagation

edited by Yiying Feng,

Jiangen Liu

, Yiming Wang and

Alex Elías-Zúñiga

submission deadline 20 Jun 2025 | 4 articles | Viewed by 1560 | Submission Open

Keywords: general fractional calculus; integration of mathematics and engineering; fractional rheological models; fractal dimensional space; nonlinear theory; fractional wave propagation models

(This special issue belongs to the Section Engineering)

Symmetry and Solutions of Fractional Differential Equations with Their Developments

edited by Lihong Zhang,

Ravi P. Agarwal

,

Bashir Ahmad

and

Guotao Wang

submission deadline 30 Jun 2025 | 12 articles | Viewed by 20510 | Submission Open

Keywords: nonlinear fractional ordinary (partial) differential equations and applications; nonlinear problem involving fractional Laplacian operators and their variants; nonlinear Hammerstein equations involving fractional operators; nonlocal Monge– Ampere equation and its extensions; nonlocal operators; symmetries; and applications; geometrical methods for problems of mathematical physics; geometrical analysis and differential equations; monotonicity of solutions to various differential equations; existence and uniqueness of solutions to differential equations; symmetry of solutions to differential equations

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

Fractional Systems, Integrals and Derivatives: Theory and Application

edited by

Andrey Zahariev

and

Hristo Kiskinov

submission deadline 30 Jun 2025 | 13 articles | Viewed by 13073 | 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)

Fractal and Multifractal Analysis in Environmental, Medical and Technical Fields: Pattern Recognition, Analysis and Processing of Images

edited by

Erveton Pinheiro Pinto

,

Marcelo Pires

and

Nilson dos Santos Ferreira

submission deadline 30 Jun 2025 | 1 articles | Viewed by 2295 | Submission Open

Keywords: fractal analysis; multifractal spectrum; lacunarity spectrum; pattern recognition; neural networks; mathematical morphology; machine learning; medical images; nature textures; surfaces; scanning probe microscopy (SPM); transmission electron microscopy (TEM); scanning electron microscopy (SEM)

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

Advanced Fractional Sliding Mode Control for Dynamic and Robotic Systems

edited by Mehran Rahmani

submission deadline 30 Jun 2025 | 2 articles | Viewed by 1845 | Submission Open

Keywords: fractional sliding mode control; robust control; dynamic systems; robotics

(This special issue belongs to the Section Engineering)

Fractal and Fractional in Construction Materials

edited by

Shengwen Tang

and

Lei Wang

submission deadline 30 Jun 2025 | 1 articles | Viewed by 1784 | Submission Open

Keywords: construction materials; fractal and fractional; mechanical performance; fractal theory; experiment; transportation; durability

(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 2025 | 1 articles | Viewed by 1566 | 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)

Multi-Scale and Fractal Research on Advanced Manufacturing and Tribology

edited by

Feng Feng

and

Qiang Li

submission deadline 30 Jun 2025 | 1 articles | Viewed by 1137 | 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)

Efficient Development of Geo-Energy and Carbon Sequestration in Fractal Geo-Systems: New Challenges

edited by Zhongwei Wu, Chuanzhi Cui and

Japan Trivedi

submission deadline 30 Jun 2025 | 1 articles | Viewed by 596 | Submission Open

Keywords: geo-energy development; fractal geometry; CCUS/CCS; data analysis technology; production enhancement technologies; multi-phase flow discipline; water– rock reaction in fractal systems

(This special issue belongs to the Section Engineering)

Fractional Order Mechatronics

edited by

Ying Luo

and Pengchong Chen

submission deadline 30 Jun 2025 | Viewed by 459 | Submission Open

Keywords: fractional-order system and control; mechatronics; fractional-order modeling; application actuators and sensors; system stability and optimization

(This special issue belongs to the Section Engineering)

Feature Papers for Numerical and Computational Methods Section 2024–2025: Analog and Digital Implementations

edited by

Riccardo Caponetto

submission deadline 30 Jun 2025 | Viewed by 209 | Submission Open

Keywords: fractional calculus; numerical methods; approximation methods; computational procedures; algorithms; digital implementation; hardware in the loop implementation; FPGA implementation; data mining with fractional calculus methods; fractional calculus with artificial intelligence applications; image/signal analyses based on fractional calculus; fuzzy fractional calculus; neural computations with fractional calculus; applications of fractional calculus in nonlinear science; applications in control; mechanics; financial mathematics; engineering; biomedicine; etc.

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

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 2025 | 2 articles | Viewed by 2236 | 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 2025 | Viewed by 375 | 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)

New Insights into Random Walks and Diffusion Equations

edited by Marco Antonio Alves Da Silva, José Carlos Cressoni and

Gandhimohan M. Viswanathan

submission deadline 18 Jul 2025 | Viewed by 332 | Submission Open

Keywords: continuous-time random walks; discrete-time random walks; diffusion equations; fractional diffusion equations; anomalous diffusion; computer simulation; markovian processes; non-markovian processes

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

Complexity, Fractality and Fractional Dynamics Applied to Science and Engineering

edited by Alexandra M.S.F. Galhano,

Sergio Adriani David

and

António Lopes

submission deadline 20 Jul 2025 | 10 articles | Viewed by 14450 | 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 Differential Operators and Their Applications, 2nd Edition

edited by

Angelo B. Mingarelli

,

Leila Gholizadeh Zivlaei

and

Mohammad Dehghan

submission deadline 25 Jul 2025 | 7 articles | Viewed by 7272 | Submission Open

Keywords: generalized derivatives; riemann– liouville; caputo derivatives; spectral theory; asymptotic theory; qualitative theory; variational theorems; applications

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

Fractal Dimensions with Applications in the Real World

edited by Jun Luo,

Xiaohao Cai

and

Liang-Yi Huang

submission deadline 31 Jul 2025 | 4 articles | Viewed by 5215 | Submission Open

Keywords: iterated function systems; self-similar sets; self-affine sets; fractal measures; fractal graphs; beta-expansions; Hausdorff dimension; box-counting dimension; Lipschitz equivalence; topological structures

(This special issue belongs to the Section Geometry)

Analysis and Numerical Computations of Nonlinear Fractional and Classical Differential Equations

edited by

Xiao-Jun Yang

, Wenxue Zhou, Sunil Dutt Purohit,

Ali Turab

and Ahmed Refaie Ali

submission deadline 31 Jul 2025 | 4 articles | Viewed by 4016 | Submission Open

Keywords: nonlinear PDEs; fractional PDEs; general fractional PDEs; fractional mathematical models; mathematical models in real-world problems; integral transforms for nonlinear problems; special functions; computational methods; numeral methods; traveling wave solutions; similarity solution; series expansion method; finite element method; finite difference method; group analysis; reduced differential transform method; differential transform method; residual power series method; homotopy analysis method; decomposition method; homotopy perturbation method; asymptotic perturbation solution; variational iteration method; coupling methods

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

Iterative Methods in Solving Nonlinear Equations Based on Fractal and Fractional Perspective

edited by

Neus Garrido

,

Francisco I. Chicharro

and

Paula Triguero-Navarro

submission deadline 31 Jul 2025 | 2 articles | Viewed by 2524 | Submission Open

Keywords: iterative methods; stability theory; methods with memory; simultaneous roots; multiple roots; fractional derivatives; fractal dimension; nonlinear dynamics; mathematical modelling

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

Delayed and Stochastic Fractional Order Dynamical Systems: Theory, Numerical Methods, Control, and Applications

edited by Andreas Basse-O'Connor, Ahmadreza Haghighi,

Hossein Jafari

and

Majid Roohi

submission deadline 31 Jul 2025 | 1 articles | Viewed by 1430 | Submission Open

Keywords: fractional calculus; delayed systems; stochastic processes; control strategies; stability analysis; signal processing; robotics; biomedical engineering; renewable energy; communication networks; economics; finance; interdisciplinary research; electrical circuits; mechanical systems; process optimization biomedical modeling

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 2025 | 1 articles | Viewed by 1301 | 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)

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 31 Jul 2025 | 1 articles | Viewed by 1051 | 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)

Journal Menu

Journal Browser

Special Issues

Further Information

Guidelines

MDPI Initiatives

Follow MDPI