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Discrete & Continuous Dynamical Systems - Series S (DCDS-S) only publishes theme issues. Each issue is devoted to a specific area of the mathematical, physical and applied sciences. This area will define a research frontier that is advancing rapidly, often bridging mathematics and sciences. DCDS-S is essential reading for mathematicians, physicists, engineers and other applied scientists.

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Preface: Special issue on recent advances in nonlinear dynamics and modelling
Zakia Hammouch, Dumitru Baleanu and Said Melliani
2021, 14(10) : i-i doi: 10.3934/dcdss.2021094 +[Abstract](17) +[HTML](13) +[PDF](70.3KB)
Oscillation criteria for kernel function dependent fractional dynamic equations
Bahaaeldin Abdalla and Thabet Abdeljawad
2021, 14(10) : 3337-3349 doi: 10.3934/dcdss.2020443 +[Abstract](590) +[HTML](268) +[PDF](338.1KB)
Applying quantum calculus for the existence of solution of $ q $-integro-differential equations with three criteria
Thabet Abdeljawad and Mohammad Esmael Samei
2021, 14(10) : 3351-3386 doi: 10.3934/dcdss.2020440 +[Abstract](811) +[HTML](268) +[PDF](470.06KB)
Mathematical modelling of cytosolic calcium concentration distribution using non-local fractional operator
Ritu Agarwal, Kritika, Sunil Dutt Purohit and Devendra Kumar
2021, 14(10) : 3387-3399 doi: 10.3934/dcdss.2021017 +[Abstract](500) +[HTML](283) +[PDF](279.61KB)
Analysis and new applications of fractal fractional differential equations with power law kernel
Ali Akgül
2021, 14(10) : 3401-3417 doi: 10.3934/dcdss.2020423 +[Abstract](686) +[HTML](354) +[PDF](911.44KB)
Androgen driven evolutionary population dynamics in prostate cancer growth
Ebraheem O. Alzahrani and Muhammad Altaf Khan
2021, 14(10) : 3419-3440 doi: 10.3934/dcdss.2020426 +[Abstract](893) +[HTML](355) +[PDF](587.86KB)
On solutions of fractal fractional differential equations
Abdon Atangana and Ali Akgül
2021, 14(10) : 3441-3457 doi: 10.3934/dcdss.2020421 +[Abstract](1112) +[HTML](457) +[PDF](1381.16KB)
Computational and numerical simulations for the deoxyribonucleic acid (DNA) model
Raghda A. M. Attia, Dumitru Baleanu, Dianchen Lu, Mostafa M. A. Khater and El-Sayed Ahmed
2021, 14(10) : 3459-3478 doi: 10.3934/dcdss.2021018 +[Abstract](560) +[HTML](216) +[PDF](7764.42KB)
On a nonlocal problem involving the fractional $ p(x,.) $-Laplacian satisfying Cerami condition
Elhoussine Azroul, Abdelmoujib Benkirane and and Mohammed Shimi
2021, 14(10) : 3479-3495 doi: 10.3934/dcdss.2020425 +[Abstract](685) +[HTML](343) +[PDF](407.47KB)
Nonlinear singular $ p $ -Laplacian boundary value problems in the frame of conformable derivative
Mokhtar Bouloudene, Manar A. Alqudah, Fahd Jarad, Yassine Adjabi and Thabet Abdeljawad
2021, 14(10) : 3497-3528 doi: 10.3934/dcdss.2020442 +[Abstract](670) +[HTML](287) +[PDF](478.95KB)
On the fuzzy stability results for fractional stochastic Volterra integral equation
Reza Chaharpashlou, Abdon Atangana and Reza Saadati
2021, 14(10) : 3529-3539 doi: 10.3934/dcdss.2020432 +[Abstract](713) +[HTML](283) +[PDF](362.66KB)
Stability analysis of a general HIV dynamics model with multi-stages of infected cells and two routes of infection
A. M. Elaiw, N. H. AlShamrani, A. Abdel-Aty and H. Dutta
2021, 14(10) : 3541-3556 doi: 10.3934/dcdss.2020441 +[Abstract](598) +[HTML](255) +[PDF](843.02KB)
Application of Caputo-Fabrizio derivative to a cancer model with unknown parameters
M. M. El-Dessoky and Muhammad Altaf Khan
2021, 14(10) : 3557-3575 doi: 10.3934/dcdss.2020429 +[Abstract](658) +[HTML](330) +[PDF](2883.92KB)
An efficient numerical method for fractional model of allelopathic stimulatory phytoplankton species with Mittag-Leffler law
Behzad Ghanbari, Devendra Kumar and Jagdev Singh
2021, 14(10) : 3577-3587 doi: 10.3934/dcdss.2020428 +[Abstract](634) +[HTML](342) +[PDF](688.48KB)
Analytical study of fractional nonlinear Schrödinger equation with harmonic oscillator
Amit Goswami, Sushila Rathore, Jagdev Singh and Devendra Kumar
2021, 14(10) : 3589-3610 doi: 10.3934/dcdss.2021021 +[Abstract](580) +[HTML](253) +[PDF](1031.21KB)
Solving a class of biological HIV infection model of latently infected cells using heuristic approach
Yolanda Guerrero–Sánchez, Muhammad Umar, Zulqurnain Sabir, Juan L. G. Guirao and Muhammad Asif Zahoor Raja
2021, 14(10) : 3611-3628 doi: 10.3934/dcdss.2020431 +[Abstract](617) +[HTML](281) +[PDF](4277.53KB)
Pata type contractions involving rational expressions with an application to integral equations
Erdal Karapınar, Abdon Atangana and Andreea Fulga
2021, 14(10) : 3629-3640 doi: 10.3934/dcdss.2020420 +[Abstract](745) +[HTML](389) +[PDF](361.42KB)
Feedback stabilization of bilinear coupled hyperbolic systems
Ilyasse Lamrani, Imad El Harraki, Ali Boutoulout and Fatima-Zahrae El Alaoui
2021, 14(10) : 3641-3657 doi: 10.3934/dcdss.2020434 +[Abstract](1009) +[HTML](381) +[PDF](380.68KB)
Asymptotic behaviors of solution to partial differential equation with Caputo–Hadamard derivative and fractional Laplacian: Hyperbolic case
Changpin Li and Zhiqiang Li
2021, 14(10) : 3659-3683 doi: 10.3934/dcdss.2021023 +[Abstract](661) +[HTML](228) +[PDF](481.97KB)
Numerical simulation of the nonlinear fractional regularized long-wave model arising in ion acoustic plasma waves
Omid Nikan, Seyedeh Mahboubeh Molavi-Arabshai and Hossein Jafari
2021, 14(10) : 3685-3701 doi: 10.3934/dcdss.2020466 +[Abstract](649) +[HTML](354) +[PDF](1077.66KB)
Some new bounds analogous to generalized proportional fractional integral operator with respect to another function
Saima Rashid, Fahd Jarad and Zakia Hammouch
2021, 14(10) : 3703-3718 doi: 10.3934/dcdss.2021020 +[Abstract](511) +[HTML](354) +[PDF](396.1KB)
Comprehensive analysis of integer-order, Caputo-Fabrizio (CF) and Atangana-Baleanu (ABC) fractional time derivative for MHD Oldroyd-B fluid with slip effect and time dependent boundary condition
Muhammad Bilal Riaz and Syed Tauseef Saeed
2021, 14(10) : 3719-3746 doi: 10.3934/dcdss.2020430 +[Abstract](745) +[HTML](443) +[PDF](5394.63KB)
Solving fractional Advection-diffusion equation using Genocchi operational matrix based on Atangana-Baleanu derivative
S. Sadeghi, H. Jafari and S. Nemati
2021, 14(10) : 3747-3761 doi: 10.3934/dcdss.2020435 +[Abstract](713) +[HTML](348) +[PDF](1133.34KB)
A robust computational framework for analyzing fractional dynamical systems
Khosro Sayevand and Valeyollah Moradi
2021, 14(10) : 3763-3783 doi: 10.3934/dcdss.2021022 +[Abstract](555) +[HTML](266) +[PDF](526.05KB)
Oscillatory states and patterns formation in a two-cell cubic autocatalytic reaction-diffusion model subjected to the Dirichlet conditions
H. M. Srivastava, H. I. Abdel-Gawad and Khaled Mohammed Saad
2021, 14(10) : 3785-3801 doi: 10.3934/dcdss.2020433 +[Abstract](755) +[HTML](289) +[PDF](580.72KB)
Class of integrals and applications of fractional kinetic equation with the generalized multi-index Bessel function
Dayalal Suthar, Sunil Dutt Purohit, Haile Habenom and Jagdev Singh
2021, 14(10) : 3803-3819 doi: 10.3934/dcdss.2021019 +[Abstract](423) +[HTML](192) +[PDF](370.28KB)
Existence and nonexistence of entire positive radial solutions for a class of Schrödinger elliptic systems involving a nonlinear operator
Zedong Yang, Guotao Wang, Ravi P. Agarwal and Haiyong Xu
2021, 14(10) : 3821-3836 doi: 10.3934/dcdss.2020436 +[Abstract](672) +[HTML](318) +[PDF](352.4KB)
On the observability of conformable linear time-invariant control systems
Awais Younus, Zoubia Dastgeer, Nudrat Ishaq, Abdul Ghaffar, Kottakkaran Sooppy Nisar and Devendra Kumar
2021, 14(10) : 3837-3849 doi: 10.3934/dcdss.2020444 +[Abstract](870) +[HTML](283) +[PDF](314.46KB)
Radial symmetry for logarithmic Choquard equation involving a generalized tempered fractional $ p $-Laplacian
Lihong Zhang, Wenwen Hou, Bashir Ahmad and Guotao Wang
2021, 14(10) : 3851-3863 doi: 10.3934/dcdss.2020445 +[Abstract](596) +[HTML](294) +[PDF](378.54KB)
WITHDRAWN: Fractional diffusion equation described by the Atangana-Baleanu fractional derivative and its approximate solution
Editorial Office
2021doi: 10.3934/dcdss.2020173 +[Abstract](222) +[HTML](114) +[PDF](45.47KB)
From quasi-incompressible to semi-compressible fluids
Tomáš Roubíček
2020doi: 10.3934/dcdss.2020414 +[Abstract](788) +[HTML](380) +[PDF](453.34KB)
Global weak solutions for an newtonian fluid interacting with a Koiter type shell under natural boundary conditions
Hannes Eberlein and Michael Růžička
2020doi: 10.3934/dcdss.2020419 +[Abstract](709) +[HTML](403) +[PDF](624.9KB)
A theory of generalised solutions for ideal gas mixtures with Maxwell-Stefan diffusion
Pierre-Etienne Druet
2020doi: 10.3934/dcdss.2020458 +[Abstract](729) +[HTML](275) +[PDF](462.63KB)
An experimentally-fitted thermodynamical constitutive model for polycrystalline shape memory alloys
Barbora Benešová, Miroslav Frost, Lukáš Kadeřávek, Tomáš Roubíček and Petr Sedlák
2020doi: 10.3934/dcdss.2020459 +[Abstract](595) +[HTML](324) +[PDF](2865.27KB)
Dimension reduction of thermistor models for large-area organic light-emitting diodes
Annegret Glitzky, Matthias Liero and Grigor Nika
2020doi: 10.3934/dcdss.2020460 +[Abstract](554) +[HTML](280) +[PDF](402.03KB)
On a linearized Mullins-Sekerka/Stokes system for two-phase flows
Helmut Abels and Andreas Marquardt
2020doi: 10.3934/dcdss.2020467 +[Abstract](531) +[HTML](252) +[PDF](420.1KB)
Stochastic delay differential equations of three-species prey-predator system with cooperation among prey species
Fathalla A. Rihan and Hebatallah J. Alsakaji
2020doi: 10.3934/dcdss.2020468 +[Abstract](917) +[HTML](273) +[PDF](1090.19KB)
Equilibrium of immersed hyperelastic solids
Manuel Friedrich, Martin Kružík and Ulisse Stefanelli
2021doi: 10.3934/dcdss.2021003 +[Abstract](456) +[HTML](211) +[PDF](369.13KB)
On properties of similarity boundary of attractors in product dynamical systems
Nitha Niralda P C and Sunil Mathew
2021doi: 10.3934/dcdss.2021004 +[Abstract](421) +[HTML](199) +[PDF](530.27KB)
Finite- and multi-dimensional state representations and some fundamental asymptotic properties of a family of nonlinear multi-population models for HIV/AIDS with ART treatment and distributed delays
Divine Wanduku
2021doi: 10.3934/dcdss.2021005 +[Abstract](484) +[HTML](219) +[PDF](1264.54KB)
Shape optimization method for an inverse geometric source problem and stability at critical shape
Lekbir Afraites, Chorouk Masnaoui and Mourad Nachaoui
2021doi: 10.3934/dcdss.2021006 +[Abstract](648) +[HTML](220) +[PDF](490.99KB)
A novel semi-analytical method for solutions of two dimensional fuzzy fractional wave equation using natural transform
Muhammad Arfan, Kamal Shah, Aman Ullah, Soheil Salahshour, Ali Ahmadian and Massimiliano Ferrara
2021doi: 10.3934/dcdss.2021011 +[Abstract](464) +[HTML](306) +[PDF](9344.18KB)
Existence and regularity results for a singular parabolic equations with degenerate coercivity
Mounim El Ouardy, Youssef El Hadfi and Aziz Ifzarne
2021doi: 10.3934/dcdss.2021012 +[Abstract](661) +[HTML](236) +[PDF](438.4KB)
An efficient D-N alternating algorithm for solving an inverse problem for Helmholtz equation
Karzan Berdawood, Abdeljalil Nachaoui, Rostam Saeed, Mourad Nachaoui and Fatima Aboud
2021doi: 10.3934/dcdss.2021013 +[Abstract](477) +[HTML](232) +[PDF](1394.52KB)
Energetics and coarsening analysis of a simplified non-linear surface growth model
Hamza Khalfi, Amal Aarab and Nour Eddine Alaa
2021doi: 10.3934/dcdss.2021014 +[Abstract](402) +[HTML](226) +[PDF](1438.14KB)
Existence of solution for Kirchhoff type problem in Orlicz-Sobolev spaces Via Leray-Schauder's nonlinear alternative
Abdelaaziz Sbai, Youssef El Hadfi, Mohammed Srati and Noureddine Aboutabit
2021doi: 10.3934/dcdss.2021015 +[Abstract](613) +[HTML](233) +[PDF](380.88KB)
A novel collocation approach to solve a nonlinear stochastic differential equation of fractional order involving a constant delay
Seddigheh Banihashemi, Hossein Jafaria and Afshin Babaei
2021doi: 10.3934/dcdss.2021025 +[Abstract](492) +[HTML](189) +[PDF](2449.35KB)
Extended Krylov subspace methods for solving Sylvester and Stein tensor equations
Abdeslem Hafid Bentbib, Smahane El-Halouy and El Mostafa Sadek
2021doi: 10.3934/dcdss.2021026 +[Abstract](379) +[HTML](263) +[PDF](548.67KB)
Fractional Laplacians : A short survey
Maha Daoud and El Haj Laamri
2021doi: 10.3934/dcdss.2021027 +[Abstract](531) +[HTML](262) +[PDF](908.36KB)
Existence results for nonlinear mono-energetic singular transport equations: $ L^p $-spaces
Khalid Latrach, Hssaine Oummi and Ahmed Zeghal
2021doi: 10.3934/dcdss.2021028 +[Abstract](484) +[HTML](162) +[PDF](485.19KB)
Positive solutions for the $ p(x)- $Laplacian : Application of the Nehari method
Said Taarabti
2021doi: 10.3934/dcdss.2021029 +[Abstract](365) +[HTML](182) +[PDF](423.32KB)
Galerkin method of weakly damped cubic nonlinear Schrödinger with Dirac impurity, and artificial boundary condition in a half-line
Abderrazak Chrifi, Mostafa Abounouh and Hassan Al Moatassime
2021doi: 10.3934/dcdss.2021030 +[Abstract](364) +[HTML](157) +[PDF](417.7KB)
Cahn–Hilliard–Brinkman systems for tumour growth
Matthias Ebenbeck, Harald Garcke and Robert Nürnberg
2021doi: 10.3934/dcdss.2021034 +[Abstract](418) +[HTML](178) +[PDF](1451.32KB)
Dependent delay stability characterization for a polynomial T-S Carbon Dioxide model
Azeddine Elmajidi, Elhoussine Elmazoudi, Jamila Elalami and Noureddine Elalami
2021doi: 10.3934/dcdss.2021035 +[Abstract](449) +[HTML](163) +[PDF](509.89KB)
Frequency domain $ H_{\infty} $ control design for active suspension systems
Jamal Mrazgua, El Houssaine Tissir and Mohamed Ouahi
2021doi: 10.3934/dcdss.2021036 +[Abstract](467) +[HTML](174) +[PDF](801.02KB)
Hyers-Ulam-Rassias stability of high-dimensional quaternion impulsive fuzzy dynamic equations on time scales
Chao Wang, Zhien Li and Ravi P. Agarwal
2021doi: 10.3934/dcdss.2021041 +[Abstract](338) +[HTML](148) +[PDF](474.78KB)
Explicit multistep stochastic characteristic approximation methods for forward backward stochastic differential equations
Ying Liu, Yabing Sun and Weidong Zhao
2021doi: 10.3934/dcdss.2021044 +[Abstract](268) +[HTML](211) +[PDF](410.12KB)
Resampled ensemble Kalman inversion for Bayesian parameter estimation with sequential data
Jiangqi Wu, Linjie Wen and Jinglai Li
2021doi: 10.3934/dcdss.2021045 +[Abstract](232) +[HTML](162) +[PDF](447.04KB)
Discrete approximation of dynamic phase-field fracture in visco-elastic materials
Marita Thomas and Sven Tornquist
2021doi: 10.3934/dcdss.2021067 +[Abstract](158) +[HTML](81) +[PDF](1035.03KB)
Controllability of Sobolev type fuzzy differential equation with non-instantaneous impulsive condition
Muslim Malik, Anjali Rose and Anil Kumar
2021doi: 10.3934/dcdss.2021068 +[Abstract](447) +[HTML](98) +[PDF](399.27KB)
A new coupled complex boundary method (CCBM) for an inverse obstacle problem
Lekbir Afraites
2021doi: 10.3934/dcdss.2021069 +[Abstract](108) +[HTML](66) +[PDF](568.79KB)
Solving the linear transport equation by a deep neural network approach
Zheng Chen, Liu Liu and Lin Mu
2021doi: 10.3934/dcdss.2021070 +[Abstract](123) +[HTML](79) +[PDF](1313.31KB)
Stable numerical methods for a stochastic nonlinear Schrödinger equation with linear multiplicative noise
Xiaobing Feng and Shu Ma
2021doi: 10.3934/dcdss.2021071 +[Abstract](127) +[HTML](56) +[PDF](2334.26KB)
An independent set degree condition for fractional critical deleted graphs
Wei Gao, Juan Luis García Guirao, Mahmoud Abdel-Aty and Wenfei Xi
2019, 12(4&5) : 877-886 doi: 10.3934/dcdss.2019058 +[Abstract](3681) +[HTML](805) +[PDF](344.92KB) Cited By(105)
Stability of the heat and of the wave equations with boundary time-varying delays
Serge Nicaise, Julie Valein and Emilia Fridman
2009, 2(3) : 559-581 doi: 10.3934/dcdss.2009.2.559 +[Abstract](4384) +[PDF](248.1KB) Cited By(68)
Recent progress in the theory of nonlinear diffusion with fractional Laplacian operators
Juan-Luis Vázquez
2014, 7(4) : 857-885 doi: 10.3934/dcdss.2014.7.857 +[Abstract](5078) +[PDF](592.6KB) Cited By(56)
Tight independent set neighborhood union condition for fractional critical deleted graphs and ID deleted graphs
Darko Dimitrov and Hosam Abdo
2019, 12(4&5) : 711-721 doi: 10.3934/dcdss.2019045 +[Abstract](3827) +[HTML](864) +[PDF](340.7KB) Cited By(43)
Non-autonomous attractors for integro-differential evolution equations
Tomás Caraballo and P.E. Kloeden
2009, 2(1) : 17-36 doi: 10.3934/dcdss.2009.2.17 +[Abstract](3926) +[PDF](245.6KB) Cited By(42)
On existence, uniform decay rates and blow up for solutions of systems of nonlinear wave equations with damping and source terms
Claudianor O. Alves, M. M. Cavalcanti, Valeria N. Domingos Cavalcanti, Mohammad A. Rammaha and Daniel Toundykov
2009, 2(3) : 583-608 doi: 10.3934/dcdss.2009.2.583 +[Abstract](4140) +[PDF](327.1KB) Cited By(39)
A new finite element scheme for Landau-Lifchitz equations
François Alouges
2008, 1(2) : 187-196 doi: 10.3934/dcdss.2008.1.187 +[Abstract](3603) +[PDF](185.3KB) Cited By(35)
Uniform energy decay for a wave equation with partially supported nonlinear boundary dissipation without growth restrictions
Moez Daoulatli, Irena Lasiecka and Daniel Toundykov
2009, 2(1) : 67-94 doi: 10.3934/dcdss.2009.2.67 +[Abstract](4059) +[PDF](368.9KB) Cited By(34)
New statistical symmetries of the multi-point equations and its importance for turbulent scaling laws
Martin Oberlack and Andreas Rosteck
2010, 3(3) : 451-471 doi: 10.3934/dcdss.2010.3.451 +[Abstract](4804) +[PDF](256.0KB) Cited By(32)
New aspects of time fractional optimal control problems within operators with nonsingular kernel
Tuğba Akman Yıldız, Amin Jajarmi, Burak Yıldız and Dumitru Baleanu
2020, 13(3) : 407-428 doi: 10.3934/dcdss.2020023 +[Abstract](4572) +[HTML](1241) +[PDF](767.59KB) Cited By(31)
Generalized fractional derivatives and Laplace transform
Fahd Jarad and Thabet Abdeljawad
2020, 13(3) : 709-722 doi: 10.3934/dcdss.2020039 +[Abstract](6437) +[HTML](1462) +[PDF](306.74KB) PDF Downloads(3854)
Self-adaptive algorithm based on a posteriori analysis of the error applied to air quality forecasting using the finite volume method
Hatim Tayeq, Amal Bergam, Anouar El Harrak and Kenza Khomsi
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Existence results for nonlinear mono-energetic singular transport equations: $ L^p $-spaces
Khalid Latrach, Hssaine Oummi and Ahmed Zeghal
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Comparing the new fractional derivative operators involving exponential and Mittag-Leffler kernel
Mehmet Yavuz and Necati Özdemir
2020, 13(3) : 995-1006 doi: 10.3934/dcdss.2020058 +[Abstract](4610) +[HTML](689) +[PDF](664.49KB) PDF Downloads(1570)
On a new fractional Sobolev space and applications to nonlocal variational problems with variable exponent
Anouar Bahrouni and VicenŢiu D. RĂdulescu
2018, 11(3) : 379-389 doi: 10.3934/dcdss.2018021 +[Abstract](7199) +[HTML](453) +[PDF](418.1KB) PDF Downloads(1402)
New exact solutions for some fractional order differential equations via improved sub-equation method
Berat Karaagac
2019, 12(3) : 447-454 doi: 10.3934/dcdss.2019029 +[Abstract](5463) +[HTML](263) +[PDF](846.56KB) PDF Downloads(1118)
Heat transfer and entropy analysis of Maxwell hybrid nanofluid including effects of inclined magnetic field, Joule heating and thermal radiation
Asim Aziz, Wasim Jamshed, Yasir Ali and Moniba Shams
2020, 13(10) : 2667-2690 doi: 10.3934/dcdss.2020142 +[Abstract](2472) +[HTML](435) +[PDF](1489.18KB) PDF Downloads(1073)
Extension of triple Laplace transform for solving fractional differential equations
Amir Khan, Asaf Khan, Tahir Khan and Gul Zaman
2020, 13(3) : 755-768 doi: 10.3934/dcdss.2020042 +[Abstract](3682) +[HTML](922) +[PDF](608.6KB) PDF Downloads(1017)
A novel predictor-corrector scheme for solving variable-order fractional delay differential equations involving operators with Mittag-Leffler kernel
Antonio Coronel-Escamilla and José Francisco Gómez-Aguilar
2020, 13(3) : 561-574 doi: 10.3934/dcdss.2020031 +[Abstract](3681) +[HTML](779) +[PDF](860.14KB) PDF Downloads(917)
Risk assessment for enterprise merger and acquisition via multiple classifier fusion
Yinying Duan, Yong Ye and Zhichao Liu
2019, 12(4&5) : 747-759 doi: 10.3934/dcdss.2019049 +[Abstract](3825) +[HTML](862) +[PDF](6101.98KB) PDF Downloads(829)

2020 Impact Factor: 2.425
5 Year Impact Factor: 1.490
2020 CiteScore: 3.1

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