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A New Stability Analysis of Uncertain Delay Differential Equations

Xiao Wang, Yufu Ning
<span title="2019-01-06">2019</span> <i title="Hindawi Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wpareqynwbgqdfodcyhh36aqaq" style="color: black;">Mathematical Problems in Engineering</a> </i> &nbsp;
This paper first provides a concept of almost sure stability for uncertain delay differential equations and analyzes this new sort of stability.  ...  Finally, the relationship between almost sure stability and stability in measure for uncertain delay differential equations is discussed.  ...  Acknowledgments This work was funded by National Natural Science Foundation of China (11701338) and a Project of Shandong Province Higher Educational Science and Technology Program (J17KB124).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1155/2019/1257386">doi:10.1155/2019/1257386</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/rqljyqp3kjdcphhmrxcfukktmq">fatcat:rqljyqp3kjdcphhmrxcfukktmq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190502000440/http://downloads.hindawi.com/journals/mpe/2019/1257386.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/63/ad/63ad9aea05f6402bf94a6ace65792deaa6b616ca.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1155/2019/1257386"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> hindawi.com </button> </a>

The existence and uniqueness theorems of fuzzy delay differential equations

Nor Atirah Izzah Zulkefli, Normah Maan
<span title="2014-08-05">2014</span> <i title="Penerbit UTM Press"> Malaysian Journal of Fundamental and Applied Sciences </i> &nbsp;
Therefore, in this paper, we propose the existence and uniqueness theorems for fuzzy time-delay dynamical systems.  ...  Delay differential equations (DDEs) arise many different phenomena including in physics, biology and chemistry.  ...  The authors are thankful for the financial support.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.11113/mjfas.v10n3.280">doi:10.11113/mjfas.v10n3.280</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/w3i6kpwdmbeh7ikqplrb6me374">fatcat:w3i6kpwdmbeh7ikqplrb6me374</a> </span>
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Recent Advance in Function Spaces and Their Applications in Fractional Differential Equations

Xinguang Zhang, Lishan Liu, Yonghong Wu, Liguang Wang
<span title="2019-05-07">2019</span> <i title="Hindawi Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/rvoz2f4y2jehxeukagl2wrnina" style="color: black;">Journal of Function Spaces</a> </i> &nbsp;
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  ...  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.  ...  Acknowledgments We would like to highly appraise the excellent works of all authors and reviewers. Xinguang Zhang Lishan Liu Yonghong Wu Liguang Wang  ... 
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Existence, uniqueness, and stability of uncertain delay differential equations with V-jump

Zhifu Jia, Xinsheng Liu, Cunlin Li
<span title="2020-08-26">2020</span> <i title="Springer Science and Business Media LLC"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/jl44n6bun5bbbn5hiczsjnxaca" style="color: black;">Advances in Difference Equations</a> </i> &nbsp;
Next, we establish an existence and uniqueness theorem of solution to the differential equations we proposed in the finite domain and the infinite domain, respectively.  ...  Once more, the concept of stability for uncertain delay differential equations with V-jump is proposed. In addition, the sufficient condition for stability theorem is derived.  ...  Authors' contributions All authors read and approved the final version of the manuscript.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1186/s13662-020-02895-4">doi:10.1186/s13662-020-02895-4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/uud5uflybbggzjsfniv275mu3y">fatcat:uud5uflybbggzjsfniv275mu3y</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200831205351/https://advancesindifferenceequations.springeropen.com/track/pdf/10.1186/s13662-020-02895-4" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/79/b1/79b12bfe02af838addeefd2511f533decd786462.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1186/s13662-020-02895-4"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> springer.com </button> </a>

Preface

Hemen Dutta
<span title="">2022</span> <i title="American Institute of Mathematical Sciences (AIMS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/fk5exokwondbhhgnzgdqz74oma" style="color: black;">Discrete and Continuous Dynamical Systems. Series S</a> </i> &nbsp;
The method converts the nonlinear fractional stochastic delay differential equation into a non-delay nonlinear fractional stochastic differential equation.  ...  The paper "EXISTENCE AND REGULARITY RESULTS FOR STOCHAS-TIC FRACTIONAL PSEUDO-PARABOLIC EQUATIONS DRIVEN BY WHITE NOISE" looks into solutions to a direct problem for a stochastic pseudo-parabolic equation  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3934/dcdss.2021170">doi:10.3934/dcdss.2021170</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/fnluhbn7u5hrzmhs2afcbmfpei">fatcat:fnluhbn7u5hrzmhs2afcbmfpei</a> </span>
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On existence and uniqueness of solutions to uncertain backward stochastic differential equations [article]

Weiyin Fei
<span title="2014-01-29">2014</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
This paper is concerned with a class of uncertain backward stochastic differential equations (UBSDEs) driven by both an m-dimensional Brownian motion and a d-dimensional canonical process with uniform  ...  The solutions of UBSDEs are the uncertain stochastic processes. Thus, the existence and uniqueness of solutions to UBSDEs with Lipschitzian coefficients are proved.  ...  Acknowledgment The author is highly grateful to two referees for their valuable comments and suggestions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1401.7403v1">arXiv:1401.7403v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/dn5kzrbojbb5rgw5a7rj7asdyq">fatcat:dn5kzrbojbb5rgw5a7rj7asdyq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200824082015/https://arxiv.org/pdf/1401.7403v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/2a/bf/2abf34f0dcd6c56d9c50281ef53166e12aa60266.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1401.7403v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Stability and estimate of solution to uncertain neutral delay systems

Alexander Domoshnitsky, Michael Gitman, Roman Shklyar
<span title="">2014</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/eop7rvdybzgldi3ukprnutulze" style="color: black;">Boundary Value Problems</a> </i> &nbsp;
New tests of stability and in the future of existence and uniqueness of boundary value problems for neutral delay systems can be obtained on the basis of this technique.  ...  The goal of this paper is to obtain stability of uncertain systems and to estimate the difference between solutions of a 'real' system with uncertain coefficients and/or delays and corresponding 'model  ...  Theorem  Let the conditions of Theorem  be fulfilled for system (), let there exist a vector γ = col{γ  , . . . , γ n } such that γ i >  for i = , . . . , n, and where the constants γ i and y ij  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1186/1687-2770-2014-55">doi:10.1186/1687-2770-2014-55</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/snai447es5cm5aytgbwf2jn5he">fatcat:snai447es5cm5aytgbwf2jn5he</a> </span>
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Partial stabilisation of large-scale discrete-time linear control systems

Peter Benner, Maribel Castillo, Enrique S. Quintana Orti
<span title="">2005</span> <i title="Inderscience Publishers"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/mvlpi4a7izattgygry5kh4ruaq" style="color: black;">International Journal of Computational Science and Engineering (IJCSE)</a> </i> &nbsp;
Huang Existence and Uniqueness of Solutions for A Class of the First Order Impulsive Dynamic Equations on Time Scales 683 H. Liu, X. Xiang and W.  ...  Yang Asymptotic Stability of Solutions Delay Differential Equations 859 Y. H. Peng Robust Control for The Time-Varying Delay Uncertain Neutral Systems 654 X. G. Yu and B. T.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1504/ijcse.2005.008907">doi:10.1504/ijcse.2005.008907</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7bcwbbhnv5bf7omtgtuz5dhkkm">fatcat:7bcwbbhnv5bf7omtgtuz5dhkkm</a> </span>
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Page 4288 of Mathematical Reviews Vol. , Issue 98G [page]

<span title="">1998</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Istvan Gy6ri (H-VESZ; Veszprém) 34 ORDINARY DIFFERENTIAL EQUATIONS 98g:34124 34K20 Wang, Quanyi (PRC-HUAQ; Quanzhou) The existence and uniqueness and stability of almost periodic solutions for functional-differential  ...  98¢:34121 oscillatory, if and only if the ordinary differential equation x\"*!) + (1/r) p(t)x =0 is oscillatory. The theorem is proved for n = 3. Theorem.  ... 
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Page 6659 of Mathematical Reviews Vol. , Issue 96k [page]

<span title="">1996</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Using standard methods the authors prove local existence and uniqueness of generalized solutions for functional-differential equations of the form $77", a, A"~*u)(t) = F(t,u(t—t)), @m F 0, a9 40, 0<+t<  ...  By means of the Lya- punov stability theorem and norm inequalities, several new delay- independent criteria are established to guarantee the asymptotic stability of the discrete time-delay systems subjected  ... 
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Page 6141 of Mathematical Reviews Vol. , Issue 2004h [page]

<span title="">2004</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Summary: “With the help of a continuation theorem based on Gaines and Mawhin’s coincidence degree theory, sufficient and realistic conditions are obtained for the global existence of positive periodic  ...  solutions for a delay differential system with feedback control.  ... 
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Page 2038 of Mathematical Reviews Vol. , Issue 98C [page]

<span title="">1998</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
This condition is given in terms of the existence of suitable solutions to an algebraic Riccati equation and a Riccati differential equation.  ...  Summary: “A new output tracking problem of a large class of ob- servable minimum-phase uncertain nonlinear systems is solved by a dynamical iterative change of coordinates and the introduction of a sliding  ... 
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Stability of fuzzy control systems with bounded uncertain delays

Zhang Yi, Pheng Ann Heng
<span title="">2002</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/7dwepyc5xbc47narcaqganu4vu" style="color: black;">IEEE transactions on fuzzy systems</a> </i> &nbsp;
Theorems are proved via the method of functional differential inequalities analysis.  ...  Conditions for global exponential stability of free fuzzy systems with uncertain delays are derived.  ...  ACKNOWLEDGMENT The authors would like to thank the referees for their many useful and valuable suggestions regarding this paper. They would also like to thank K. S. Leung for his helpful discussions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/91.983283">doi:10.1109/91.983283</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2yra7knqn5gvdpinqenuxedusq">fatcat:2yra7knqn5gvdpinqenuxedusq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190303042625/http://pdfs.semanticscholar.org/af37/84d492fb6eebc8c5e75218b955dc9e9d1212.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/af/37/af3784d492fb6eebc8c5e75218b955dc9e9d1212.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/91.983283"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Fuzzy delay predator-prey system: existence theorem and oscillation property of solution

Khabat Barzinji, Normah Maan, Nor'aini Aris
<span title="">2014</span> <i title="Hikari, Ltd."> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/4vhaxopflnexvdocphwuoxg3gm" style="color: black;">International Journal of Mathematical Analysis</a> </i> &nbsp;
This paper discusses the existence of solution for a fuzzy delay predator-prey system.  ...  First, we prove the existence theorem of at least one solution of fuzzy predator-prey system where the initial condition Khabat Barzinji, Normah Maan and Nor'aini Aris is also described by a fuzzy number  ...  The authors are thankful for the financial supports.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.12988/ijma.2014.4373">doi:10.12988/ijma.2014.4373</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/d66ilibbzzag7j5gps5ue33y5m">fatcat:d66ilibbzzag7j5gps5ue33y5m</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170829224709/http://www.m-hikari.com/ijma/ijma-2014/ijma-17-20-2014/barzinjiIJMA17-20-2014.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/b5/d9/b5d9ef24c1ba8d6f8f9f7e4f250e2c6b9dade21a.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.12988/ijma.2014.4373"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Page 1968 of Mathematical Reviews Vol. , Issue 96c [page]

<span title="">1996</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
In order to solve it, one has to prove a density theorem, which amounts to a uniqueness theorem, where we use a uniqueness theorem of Mizohata and regularity theorems of Gavalluci and Matsuzawa.” 96c:93134  ...  for the corresponding forward Zakai equation and a backward adjoint equation.  ... 
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