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On a class of non-linear delay distributed order fractional diffusion equations

V.G. Pimenov, A.S. Hendy, R.H. De Staelen
2017 Journal of Computational and Applied Mathematics  
In this paper, we consider a numerical scheme for a class of non-linear time delay fractional diffusion equations with distributed order in time.  ...  The derivation of a linearized difference scheme with convergence order is the main purpose of this study. Numerical experiments are carried out to support the obtained theoretical results.  ...  Acknowledgment For the first two authors, this work was supported by Act 211 Government of the Russian Federation program 02.A03.21.0006 on 27.08.2013.  ... 
doi:10.1016/j.cam.2016.02.039 fatcat:iziv2it5fbhq5od5gue7ltvsty

Page 1447 of Mathematical Reviews Vol. , Issue 2001C [page]

2001 Mathematical Reviews  
fractional trans- formation (172-175); pad d. pi sir Cuihong Yang, On the non-constant periodic orbits of cubic Kolmogorov systems of a class in R* (176-180).  ...  (367-370); Daoyi Xu, Global attractor of reaction-diffusion equations with delays (371-377); Xingwang Xu, On non-existence of positive solutions of nonlinear polyharmonic equations (378-382); Yuantong  ... 

Power Law Type Long Memory Behaviors Modeled with Distributed Time Delay Systems

Jocelyn Sabatier
2019 Fractal and Fractional  
This paper studies a class of distributed time delay systems that exhibit power law type long memory behaviors.  ...  In the literature, the analysis of distributed delay models and integro-differential equations in general is older than that of fractional models.  ...  Conflicts of Interest: The authors declare no conflict of interest. Fractal Fract. 2020, 4, 1  ... 
doi:10.3390/fractalfract4010001 fatcat:fyj75op7yvaynochlc2pdnowzy

Recent Advance in Function Spaces and Their Applications in Fractional Differential Equations

Xinguang Zhang, Lishan Liu, Yonghong Wu, Liguang Wang
2019 Journal of Function Spaces  
for a class of nonlinear time fractional partial differential equations with delay by using the theory of solution operator and the general Banach contraction mapping principle.  ...  In the paper titled "Existence Results for a Class of Semilinear Fractional Partial Differential Equations with Delay in Banach Spaces", the authors consider the existence and uniqueness of the mild solutions  ...  Acknowledgments We would like to highly appraise the excellent works of all authors and reviewers. Xinguang Zhang Lishan Liu Yonghong Wu Liguang Wang  ... 
doi:10.1155/2019/5719808 fatcat:mwdi7rybjvabjot56zpesc6f7a

Page 7196 of Mathematical Reviews Vol. , Issue 2004i [page]

2004 Mathematical Reviews  
One is a stochastic linear diffusion-reaction equation: 8,u(x,t) =O2u—Au+on(x), (x,t) €(0,L)xR*, u(0,t)=u(L,t)=0 and u(x,0)=y(x) with white noise n(x); and the other is a nonlinearly perturbed stochastic  ...  (E-SEVL-ED; Seville) ; Real, José [Real Anguas, José] (E-SEVL-ED; Seville) Existence and uniqueness of solutions for delay stochastic evolution equations of second order in time.  ... 

List of contents and Author Index, Volume 19, 2006

2006 Applied Mathematics Letters  
Pituk 320 Linearized oscillation in a nonautonomous scalar delay differential equation M.F. Furtado 326 A note on the number of nodal solutions of an elliptic equation with symmetry Y.-M.  ...  Koyunbakan 995 A new inverse problem for the diffusion operator H. Lian and W. Ge 1000 Solvability for second-order three-point boundary value problems on a half-line A.-M.  ...  Guy 873 Lagrange characteristic method for solving a class of nonlinear partial differential equations of fractional order B.C.  ... 
doi:10.1016/s0893-9659(06)00219-9 fatcat:yaqob7cf6jenxoegamqj6icw5u

Functional Differential and Difference Equations with Applications 2013

J. Diblík, E. Braverman, I. Györi, Yu. Rogovchenko, M. Růžičková, A. Zafer
2014 Abstract and Applied Analysis  
This annual issue comes as a sequel to two special issues, Recent Progress in Differential and Difference Equations edited by the four members of the present team and Functional Differential and Difference  ...  Equations with Applications with the same editorial team, both published by the Abstract and Applied Analysis in 2011 and 2012, respectively.  ...  Existence of oscillating solutions for half-linear differential equations with delay and for even order damped equations with distributed deviating arguments is studied.  ... 
doi:10.1155/2014/543797 fatcat:ijhfv4ccljga3hivsbwuwizj3i

Periodic traveling waves in SIRS endemic models

Tong Li, Yi Li, Herbert W. Hethcote
2009 Mathematical and computer modelling  
Specifically, we found that the ratio of the delay ω in the recovered class and the average infectious period 1/γ must be sufficiently large for Hopf bifurcation to occur.  ...  model without a delay.  ...  The research of Yi Li is supported in part of the  ... 
doi:10.1016/j.mcm.2008.07.033 fatcat:n3vh3vnzmrcobd7sfk4nx7ercq

Page 2270 of Mathematical Reviews Vol. , Issue 86f [page]

1986 Mathematical Reviews  
Sosnowski, Remarks on observer design for a class of linear hereditary systems with disturbances (pp. 215-221); F.  ...  El-Zahaby, Distributed control of a system governed by Dirichlet and Neumann problems for elliptic equations of infinite order (pp. 83-87); R. Gabasov, F. M. Kirillova, S. V. Gnevko and V. Z.  ... 

Understanding the Nature of the Long-Range Memory Phenomenon in Socioeconomic Systems

Rytis Kazakevičius, Aleksejus Kononovicius, Bronislovas Kaulakys, Vygintas Gontis
2021 Entropy  
Research has lead us to question whether the observed long-range memory is a result of the actual long-range memory process or just a consequence of the non-linearity of Markov processes.  ...  As our most recent result, we discuss the long-range memory of the order flow data in the financial markets and other social systems from the perspective of the fractional Lèvy stable motion.  ...  Now lets introduce non-linearity into Equation (12) .  ... 
doi:10.3390/e23091125 pmid:34573750 pmcid:PMC8470578 fatcat:dm6utaxqzfefxidlhlfmitzvkq

Fractional-order systems

2004 Second IEEE International Conference on Computational Cybernetics, 2004. ICCC 2004.  
The comprehensive ranking orders are CSW, CSC, CSML, CSP, and CS in a descending manner.  ...  Stanisz of the University of Toronto about diffusion in the bovine optic nerve and the work he published in [35].  ...  System Description In this paper, a class of fractional complex networks with time-varying delays is considered.  ... 
doi:10.1109/icccyb.2004.1437743 fatcat:yesyyjpmjbgbxede4wmgeocrqa

Page 855 of Mathematical Reviews Vol. , Issue 2000a [page]

2000 Mathematical Reviews  
Summary: “The authors prove existence of a stable transfer func- tion satisfying the nonlinear equations characterizing an asymp- totic stationary point, in the undermodeled cases, for a class of pseudo-linear  ...  The authors consider a special variant of the linear Gaussian fil- tering problem, differing from the usual problem in that the signal process has Gaussian fractional Brownian motion as the diffusive term  ... 

2013 Index IEEE Transactions on Automatic Control Vol. 58

2013 IEEE Transactions on Automatic Control  
., see Dominguez- Garcia, A. D., TAC March 2013 1696-1706 Hammouri, H., see Nadri, M., TAC March 2013 757-762 Hammouri, H., see Benachour, M. S., TAC Dec. 2013 3011-3023 Han, Q.  ...  ., +, TAC April 2013 1074-1080 Diffusion A Strict Control Lyapunov Function for a Diffusion Equation With Time- Varying Distributed Coefficients.  ...  ., +, TAC Aug. 2013 2142-2148 A Strict Control Lyapunov Function for a Diffusion Equation With Time-Varying Distributed Coefficients.  ... 
doi:10.1109/tac.2013.2295962 fatcat:3zpqog4r4nhoxgo4vodx4sj3l4

Particle size measurement of lipoprotein fractions using diffusion-ordered NMR spectroscopy

Roger Mallol, Miguel A. Rodríguez, Mercedes Heras, Maria Vinaixa, Núria Plana, Lluís Masana, Gareth A. Morris, Xavier Correig
2012 Analytical and Bioanalytical Chemistry  
We performed a pulsed-field gradient experiment on each fraction to obtain a mean diffusion coefficient, and then determined the apparent hydrodynamic radius using the Stokes-Einstein equation.  ...  To validate the hydrodynamic radii obtained, the particle size distribution of these lipoprotein fractions was also measured using transmission electron microscopy (TEM).  ...  Marimon for their assistance with the TEM analysis of the lipoprotein fractions as well as Dr. S. Pujol for her assistance with viscosity measurements.  ... 
doi:10.1007/s00216-011-5705-9 pmid:22293969 fatcat:fp25tqy4ejh4dgv6wnjgde25a4

Applications of Distributed-Order Fractional Operators: A Review

Wei Ding, Sansit Patnaik, Sai Sidhardh, Fabio Semperlotti
2021 Entropy  
Distributed-order fractional calculus (DOFC) is a rapidly emerging branch of the broader area of fractional calculus that has important and far-reaching applications for the modeling of complex systems  ...  In recent years, a significant amount of studies focusing on mathematical aspects and real-world applications of DOFC have been produced.  ...  Further, within each of these classes, further subdivisions exist depending on the specific functions chosen for (a) weights of the order-distribution functions and (b) bounds of the fractional-order α  ... 
doi:10.3390/e23010110 pmid:33467618 pmcid:PMC7830465 fatcat:twhf4c73dbbnhkveflg43r3rz4
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