Fractal and Fractional

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 2828 | 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 | 1 articles | Viewed by 814 | 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 395 | 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 | 11 articles | Viewed by 17927 | 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 | 10 articles | Viewed by 9801 | 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)

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 | 10 articles | Viewed by 7025 | 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)

Fractal Dimensions with Applications in the Real World

edited by Jun Luo,

Xiaohao Cai

and

Liang-Yi Huang

submission deadline 31 Jul 2025 | 6 articles | Viewed by 6854 | 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)

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 2971 | 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)

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 1731 | 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)

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 1644 | 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

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 1362 | 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)

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 Jul 2025 | 1 articles | Viewed by 1084 | 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)

Recent Computational Methods for Fractal and Fractional Nonlinear Partial Differential Equations

edited by

Kang-Jia Wang

and

Inés Tejado

submission deadline 31 Jul 2025 | 2 articles | Viewed by 1064 | 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)

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

edited by

Hengfei Ding

, Changpin Li and Min Cai

submission deadline 31 Jul 2025 | 1 articles | Viewed by 592 | 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)

Advances in Dynamics and Control of Fractional-Order Systems

edited by Ruihong Li

submission deadline 31 Jul 2025 | Viewed by 248 | 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)

Advances in Fractional Initial and Boundary Value Problems

edited by

Sotiris K. Ntouyas

,

Bashir Ahmad

and

Jessada Tariboon

submission deadline 1 Aug 2025 | 3 articles | Viewed by 1503 | 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)

Recent Advances in Nonlocal Problems Involving the Fractional Laplacian Operators

edited by

Yun-Ho Kim

submission deadline 14 Aug 2025 | 4 articles | Viewed by 2484 | 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)

Bifurcation, Chaos, and Fractals in Fractional-Order Electrical and Electronic Systems

edited by Faqiang Wang,

Shaobo He

and Hongbo Cao

submission deadline 15 Aug 2025 | 7 articles | Viewed by 14826 | Submission Open

Keywords: bifurcation and its control; chaos and its control; fractals and their control; fractional-order inductor/capacitor; fractional-order memristor/meminductor/memcapacitor; fractional-order circuits and systems; fractional-order electrical and electronic systems; multi-timescale and entropy analysis; fractional calculus applications

(This special issue belongs to the Section Complexity)

Fractional-Order Circuits, Systems, and Signal Processing, 2nd Edition

edited by

Norbert Herencsar

,

Shibendu Mahata

,

Esteban Tlelo-Cuautle

and

Ivo Petráš

submission deadline 15 Aug 2025 | 6 articles | Viewed by 8726 | Submission Open

Keywords: fractional-order analog filters; oscillators; PLLs; fractional-order filters for digital signal and image processing; fractional-order neural networks for signal processing; modeling of fractance behavior using active/passive elements; fabrication of fractance elements; fractional-order modeling of batteries; fractional-order control systems; fractional-order bioimpedance modeling

(This special issue belongs to the Section Engineering)

Contemporary Methods of Fractional Order Differential and Differential-Operator Equations

edited by

Sabir Umarov

,

Yuri Luchko

and

Yangquan Chen

submission deadline 22 Aug 2025 | 7 articles | Viewed by 4955 | Submission Open

Keywords: fractional-order PDEs; fractional-order differential operator equations; fractional-order SDEs; fractional fokker– planck equation; fractional-order systems; inverse problems for fractional-order equations; stability of fractional-order systems; applied fractional-order equations; applied fractional-order systems; determination of order(s); determination of coefficients; solution spaces; representation of solution; fundamental solution; mittag– leffler- and wright-type functions; matrix-valued mittag– leffler and Wright functions

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

Advances in Fractional Operators: Mathematical Perspectives and Multidisciplinary Applications

edited by Leandro Tavares and

J. Vanterler Da C. Sousa

submission deadline 25 Aug 2025 | 4 articles | Viewed by 1659 | Submission Open

Keywords: fractional equations; fractional operators; critical point theory; variational methods; fractional derivatives; Ψ -Hilfer fractional derivative; Mittag-Leffler function; generalized Mittag-Leffler function

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

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 Aug 2025 | 2 articles | Viewed by 1473 | 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)

Nonlinear Fractional Maps: Dynamics and Control

edited by Telksnys Tadas

submission deadline 25 Aug 2025 | 1 articles | Viewed by 870 | Submission Open

(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 30 Aug 2025 | 3 articles | Viewed by 2281 | 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)

Analysis of Fractional Stochastic Differential Equations and Their Applications

edited by Zhiguo Luo and Danfeng Luo

submission deadline 31 Aug 2025 | 10 articles | Viewed by 9432 | Submission Open

Keywords: fractional differential equations; stochastic differential equations; delay differential equations; impulsive differential equations; fuzzy differential equations; stability analysis; averaging principle; controllability; averaging principle; existence or uniqueness

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

Fractal and Multifractal Analysis in Econometric Models and Empirical Finance

edited by

Sun-Yong Choi

submission deadline 31 Aug 2025 | 4 articles | Viewed by 6789 | Submission Open

Keywords: multifractal analysis; hurst exponent; multiscale analysis; financial market efficiency; empirical finance

(This special issue belongs to the Section Mathematical Physics)

Continuous/Discrete-Time Fractional Systems: Modelling, Design and Estimation

edited by

Gabriel Bengochea

and

Manuel Duarte Ortigueira

submission deadline 31 Aug 2025 | 5 articles | Viewed by 6507 | Submission Open

Keywords: autoregressive-moving average (ARMA); shift-invariant; scale-invariant; fBm; Liouville; Liouville– Caputo; Hadamard; Riemann– Liouville; Dzherbashian– Caputo; Grunwald– Letnikov; two-sided Riesz– Feller derivatives

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

Fractional Integral Inequalities and Applications, 3rd Edition

edited by

Artion Kashuri

and

Hari Mohan Srivastava

submission deadline 31 Aug 2025 | 6 articles | Viewed by 5555 | 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)

Fractal and Fractional Statistics for Artificial Intelligence, Data Science, and Quantum Computing, 2nd Edition

edited by

Victor Leiva

and

Cecília Castro

submission deadline 31 Aug 2025 | 2 articles | Viewed by 2765 | Submission Open

Keywords: artificial intelligence; big data; blockchain; data science; deep learning; fractal statistics; fractional statistical moments; fractional statistics; fractional stochastic differential equations; fractile/quantile regression; fuzzy logic; multivariate statistics; quantum annealing; quantum computing; quantum information; quantum machine learning; quantum statistics; software development; statistical learning; statistical modeling

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

Analysis and Applications of Fractional Calculus in Computational Physics

edited by

Slobodanka Galovic

and

Dalibor Chevizovich

submission deadline 31 Aug 2025 | Viewed by 304 | Submission Open

Keywords: fractional calculus in physics; fractional operators; integral transformations of irrational functions; inverse Laplace transform of irrational functions; time-delayed fractional models; numerical methods in fractional problems

(This special issue belongs to the Section Mathematical Physics)

Advances in Fractional-Order Multiagent Systems: Theory and Applications

edited by Ping Gong

submission deadline 15 Sep 2025 | 8 articles | Viewed by 15377 | Submission Open

Keywords: fractional-order dynamics; multiagent systems; distributed coordination control; nonlinear control; stability analysis; algorithm design

(This special issue belongs to the Section Engineering)

New Developments in Tracking and Stabilization of Fractional-Order Systems

edited by Sakthivel Ramalingam and

Parivallal Arumugam

submission deadline 15 Sep 2025 | 3 articles | Viewed by 3377 | Submission Open

Keywords: robust control of fractional-order cyber– physical systems; tracking control of fractional-order systems; stabilization of fractional-order systems; fractional-order time delay systems; disturbance rejection of fractional order systems; optimal control of fractional-order systems; event-triggered control for fractional order systems; fractional-order networked control systems; fractional-order neural networks; fractional-order fuzzy systems

(This special issue belongs to the Section Engineering)

Fractional Porous Medium Type and Related Equations

edited by Petra Wittbold

submission deadline 15 Sep 2025 | 1 articles | Viewed by 640 | Submission Open

Keywords: time-fractional porous medium and related equations; subdiffusion processes; memory effects; stochastic perturbation; numerical approximation

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

Fractal Theory and Models in Nonlinear Dynamics and Their Applications, 2nd Edition

edited by

Luis Manuel Palacios-Pineda

and

Oscar Martínez-Romero

submission deadline 15 Sep 2025 | Viewed by 142 | Submission Open

Keywords: fractal theory; multifractals; fractal– fractional calculus; fractional chaotic systems; fractional nonlinear dynamics

(This special issue belongs to the Section Mathematical Physics)

Numerical Solutions of Caputo-Type Fractional Differential Equations and Derivatives

edited by Phumlani Dlamini and Simphiwe Simelane

submission deadline 30 Sep 2025 | 14 articles | Viewed by 16371 | 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 | 8 articles | Viewed by 11185 | 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)

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 30 Sep 2025 | 4 articles | Viewed by 3217 | 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)

Calculus of Variations, Fractional Calculus and Their Applications

edited by

Matheus J. Lazo

submission deadline 30 Sep 2025 | Viewed by 243 | Submission Open

Keywords: fractional calculus of variations; fractional derivatives and integrals; necessary and sufficient optimality conditions; fractional Euler– Lagrange equation; numerical and analytical methods; applications of fractional calculus of variations

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

Fractal and Fractional in Geotechnical Engineering, Second Edition

edited by Shaoheng He, Zhi Ding and

Panpan Guo

submission deadline 30 Sep 2025 | Viewed by 239 | Submission Open

Keywords: fractal dimension; fractional-order mechanics; micro-to-Macro analysis; geomaterial; tunnel; rock; concrete; foamed light soil; bituminous mixture

(This special issue belongs to the Section Engineering)

Fractional Nonlinear Dynamics in Science and Engineering

edited by

Jorge E. Macías Díaz

and

Tassos Bountis

submission deadline 30 Sep 2025 | Viewed by 238 | Submission Open

Keywords: nonlinear fractional models; deterministic and stochastic models; fractional nonlinear systems; dynamics of fractional nonlinear systems; complex systems

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

Fractional Derivatives in Mathematical Modeling and Applications

edited by

Damian Słota

,

Rafal Brociek

and

Edyta Hetmaniok

submission deadline 30 Sep 2025 | Viewed by 156 | 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 | Viewed by 141 | 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 22246 | 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 | 7 articles | Viewed by 4157 | 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 776 | 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 | 5 articles | Viewed by 10322 | 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 7714 | 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 5901 | 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)

Fractal Functions: Theoretical Research and Application Analysis

edited by Yong-Shun Liang and Jia Liu

submission deadline 31 Oct 2025 | 4 articles | Viewed by 2624 | Submission Open

Keywords: iterated function systems; fractal interpolation functions; fractal functions; fractal surfaces; fractional calculus; function spaces; self-similar sets and measures; self-affine and self-conformal sets/measures; fractal approximation and modeling; quantization dimension; box dimension; Hausdorff dimension; and L^q dimensions; applications of the fractal functions to any areas of finance; engineering; economy; biology; etc.

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

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

edited by

Bipan Hazarika

submission deadline 31 Oct 2025 | 2 articles | Viewed by 1710 | 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)

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