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Journal articles on the topic 'Integral delay equations'

Author: Grafiati
Published: 4 June 2021
Last updated: 18 February 2022

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1

Burton, T. A. "Integral equations with a delay." Acta Mathematica Hungarica 72, no. 3 (1996): 233–42. http://dx.doi.org/10.1007/bf00050686.

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2

Gilsinn, David E., and Florian A. Potra. "Integral Operators and Delay Differential Equations." Journal of Integral Equations and Applications 18, no. 3 (September 2006): 297–336. http://dx.doi.org/10.1216/jiea/1181075393.

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3

Li, Xiaoxuan. "Volterra Integral Equations with Vanishing Delay." Applied and Computational Mathematics 4, no. 3 (2015): 152. http://dx.doi.org/10.11648/j.acm.20150403.18.

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4

Karakostas, George, I. P. Stavroulakis, and Yumei Wu. "Oscillations of Volterra integral equations with delay." Tohoku Mathematical Journal 45, no. 4 (1993): 583–605. http://dx.doi.org/10.2748/tmj/1178225851.

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5

Xu, Dao Yi. "Integro-differential equations and delay integral inequalities." Tohoku Mathematical Journal 44, no. 3 (1992): 365–78. http://dx.doi.org/10.2748/tmj/1178227303.

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6

Melchor-Aguilar, Daniel, Vladimir Kharitonov, and Rogelio Lozano. "Lyapunov-Krasovskii functionals for integral delay equations." IFAC Proceedings Volumes 36, no. 19 (September 2003): 23–28. http://dx.doi.org/10.1016/s1474-6670(17)33296-2.

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7

Yatsenko, Yuri. "Volterra integral equations with unknown delay time." Methods and Applications of Analysis 2, no. 4 (1995): 408–19. http://dx.doi.org/10.4310/maa.1995.v2.n4.a3.

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8

BRUNNER, H. "Fully Discrete Galerkin Method For Fredholm Integro-Differential Equations With Weakly Singular Kernels." Computational Methods in Applied Mathematics 8, no. 3 (2008): 207–22. http://dx.doi.org/10.2478/cmam-2008-0015.

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AbstractWe analyze the optimal superconvergence properties of piecewise polynomial collocation solutions on uniform meshes for Volterra integral and integrodifferential equations with multiple (vanishing) proportional delays. It is shown that for delay integro-differential equations the recently obtained optimal order is also attainable. For integral equations with multiple vanishing delays this is no longer true.
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9

Liang, Jin, and Ti-Jun Xiao. "Solutions to abstract integral equations and infinite delay evolution equations." Bulletin of the Belgian Mathematical Society - Simon Stevin 18, no. 5 (November 2011): 793–804. http://dx.doi.org/10.36045/bbms/1323787167.

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10

El-Sayed, Ahmed M. A., and Yasmin M. Y. Omar. "Chandrasekhar quadratic and cubic integral equations via Volterra-Stieltjes quadratic integral equation." Demonstratio Mathematica 54, no. 1 (January 1, 2021): 25–36. http://dx.doi.org/10.1515/dema-2021-0003.

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Abstract In this work, we study the existence of one and exactly one solution x ∈ C [ 0 , 1 ] x\in C\left[0,1] , for a delay quadratic integral equation of Volterra-Stieltjes type. As special cases we study a delay quadratic integral equation of fractional order and a Chandrasekhar cubic integral equation.
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11

Journal, Baghdad Science. "Application of delay integral equations in population growth." Baghdad Science Journal 6, no. 2 (June 7, 2009): 401–4. http://dx.doi.org/10.21123/bsj.6.2.401-404.

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In this paper, the delay integral equations in population growth will be described,discussed , studied and transfered this model to integro-differential equation. At last,we will solve this problem by using variational approach.
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12

Islam, M. N. "On Infinite Delay Integral Equations Having Nonlinear Perturbations." Journal of Integral Equations and Applications 5, no. 2 (June 1993): 211–19. http://dx.doi.org/10.1216/jiea/1181075744.

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13

Prakash, P., and V. Kalaiselvi. "Fuzzy Volterra integral equations with in-finite delay." Tamkang Journal of Mathematics 40, no. 1 (March 31, 2009): 19–29. http://dx.doi.org/10.5556/j.tkjm.40.2009.33.

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14

Franco, Daniel, and Donal O'Regan. "Solutions of Volterra integral equations with infinite delay." Mathematische Nachrichten 281, no. 3 (March 2008): 325–36. http://dx.doi.org/10.1002/mana.200510605.

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15

Rahimkhani, Parisa, and Yadollah Ordokhani. "Numerical Solution of Volterra–Hammerstein Delay Integral Equations." Iranian Journal of Science and Technology, Transactions A: Science 44, no. 2 (March 20, 2020): 445–57. http://dx.doi.org/10.1007/s40995-020-00846-y.

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16

Fofana, M. S. "Moment Lyapunov exponent of delay differential equations." International Journal of Mathematics and Mathematical Sciences 30, no. 6 (2002): 339–51. http://dx.doi.org/10.1155/s0161171202012103.

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The aim of this paper is to establish a connecting thread through the probabilistic concepts ofpth-moment Lyapunov exponents, the integral averaging method, and Hale's reduction approach for delay dynamical systems. We demonstrate this connection by studying the stability of perturbed deterministic and stochastic differential equations with fixed time delays in the displacement and derivative functions. Conditions guaranteeing stable and unstable solution response are derived. It is felt that the connecting thread provides a unified framework for the stability study of delay differential equations in the deterministic and stochastic sense.
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17

Ezzinbi, Khalil, and James H. Liu. "Periodic solutions of non-densely defined delay evolution equations." Journal of Applied Mathematics and Stochastic Analysis 15, no. 2 (January 1, 2002): 105–14. http://dx.doi.org/10.1155/s1048953302000114.

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We study the finite delay evolution equation {x'(t)=Ax(t)+F(t,xt), t≥0,x0=ϕ∈C([−r,0],E), where the linear operator A is non-densely defined and satisfies the Hille-Yosida condition. First, we obtain some properties of “integral solutions” for this case and prove the compactness of an operator determined by integral solutions. This allows us to apply Horn's fixed point theorem to prove the existence of periodic integral solutions when integral solutions are bounded and ultimately bounded. This extends the study of periodic solutions for densely defined operators to the non-densely defined operators. An example is given.
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18

Wiener, Joseph, and Lokenath Debnath. "Partial differential equations with piecewise constant delay." International Journal of Mathematics and Mathematical Sciences 14, no. 3 (1991): 485–96. http://dx.doi.org/10.1155/s0161171291000674.

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The influence of certain discontinuous delays on the behavior of solutions to partial differential equations is studied. In Section 2, the initial value problems (IVP) are discussed for differential equations with piecewise constant argument (EPCA) in partial derivatives. A class of loaded partial differential equations that arise in solving certain inverse problems is studied in some detail in Section 3. Section 4 is devoted to obtain the solutions ofIVPfor linear partial differential equations with piecewise constant delay by using integral transforms. Finally, an abstract Cauchy problem is discussed.
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19

YAO, Hui-li, Chun-ying LING, and Zuo-xian FU. "Asymptotically Almost Periodic Solutions for Some Delay Integral Equations." Acta Analysis Functionalis Applicata 15, no. 2 (2013): 172. http://dx.doi.org/10.3724/sp.j.1160.2013.00172.

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20

Bellour, Azzeddine, and Mahmoud Bousselsal. "A Taylor collocation method for solving delay integral equations." Numerical Algorithms 65, no. 4 (May 21, 2013): 843–57. http://dx.doi.org/10.1007/s11075-013-9717-8.

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21

Fink, A. M., and J. A. Gatica. "Positive almost periodic solutions of some delay integral equations." Journal of Differential Equations 83, no. 1 (January 1990): 166–78. http://dx.doi.org/10.1016/0022-0396(90)90073-x.

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22

Messina, E., E. Russo, and A. Vecchio. "A convolution test equation for double delay integral equations." Journal of Computational and Applied Mathematics 228, no. 2 (June 2009): 589–99. http://dx.doi.org/10.1016/j.cam.2008.03.047.

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23

Baker, Christopher T. H., and Evgeny I. Parmuzin. "Analysis via Integral Equations of an Identification Problem for Delay Differential Equations." Journal of Integral Equations and Applications 16, no. 2 (June 2004): 111–35. http://dx.doi.org/10.1216/jiea/1181075271.

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24

Liu, Xian-Yong, Yan-Ping Liu, and Zeng-Wen Wu. "Computer simulation of pantograph delay differential equations." Thermal Science 25, no. 2 Part B (2021): 1381–85. http://dx.doi.org/10.2298/tsci200220037l.

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Ritz method is widely used in variational theory to search for an approximate solution. This paper suggests a Ritz-like method for integral equations with an emphasis of pantograph delay equations. The unknown parameters involved in the trial solution can be determined by balancing the fundamental terms.
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25

Ishiwata, Emiko, and Yoshiaki Muroya. "On collocation methods for delay differential and Volterra integral equations with proportional delay." Frontiers of Mathematics in China 4, no. 1 (February 13, 2009): 89–111. http://dx.doi.org/10.1007/s11464-009-0004-x.

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26

Kamont, Z., and S. Kozieł. "First Order Partial Functional Differential Equations with Unbounded Delay." gmj 10, no. 3 (September 2003): 509–30. http://dx.doi.org/10.1515/gmj.2003.509.

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Abstract The phase space for nonlinear hyperbolic functional differential equations with unbounded delay is constructed. The set of axioms for generalized solutions of initial problems is presented. A theorem on the existence and continuous dependence upon initial data is given. The Cauchy problem is transformed into a system of integral functional equations. The existence of solutions of this system is proved by the method of successive approximations and by using theorems on integral inequalities. Examples of phase spaces are given.
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27

Fedorov, V. E., and E. A. Omel’chenko. "Linear equations of the Sobolev type with integral delay operator." Russian Mathematics 58, no. 1 (January 2014): 60–69. http://dx.doi.org/10.3103/s1066369x14010071.

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28

Cahlon, Baruch. "Numerical solutions for functional integral equations with state-dependent delay." Applied Numerical Mathematics 9, no. 3-5 (April 1992): 291–305. http://dx.doi.org/10.1016/0168-9274(92)90023-7.

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29

Cahlon, Baruch, and Darrell Schmidt. "Stability criteria for certain delay integral equations of Volterra type." Journal of Computational and Applied Mathematics 84, no. 2 (October 1997): 161–88. http://dx.doi.org/10.1016/s0377-0427(97)00115-5.

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30

Henríquez, Hernán R., and Carlos Lizama. "Compact almost automorphic solutions to integral equations with infinite delay." Nonlinear Analysis: Theory, Methods & Applications 71, no. 12 (December 2009): 6029–37. http://dx.doi.org/10.1016/j.na.2009.05.042.

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31

Brunner, Hermann. "Iterated collocation methods for Volterra integral equations with delay arguments." Mathematics of Computation 62, no. 206 (May 1, 1994): 581. http://dx.doi.org/10.1090/s0025-5718-1994-1213835-8.

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32

Li, Bingtuan. "Multiple Integral Average Conditions for Oscillation of Delay Differential Equations." Journal of Mathematical Analysis and Applications 219, no. 1 (March 1998): 165–78. http://dx.doi.org/10.1006/jmaa.1997.5811.

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33

Yatsenko, Yuri. "Maximum principle for Volterra integral equations with controlled delay time." Optimization 53, no. 2 (April 2004): 177–87. http://dx.doi.org/10.1080/02331930410001699919.

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34

Dyson, Janet, and Rosanna Villella-Bressan. "On integral solutions on nonautonomous delay equations and their propagation." Nonlinear Analysis: Theory, Methods & Applications 24, no. 5 (March 1995): 693–710. http://dx.doi.org/10.1016/0362-546x(94)00094-x.

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35

Chen, Yueli, and Jian Xu. "Applications of the integral equation method to delay differential equations." Nonlinear Dynamics 73, no. 4 (May 21, 2013): 2241–60. http://dx.doi.org/10.1007/s11071-013-0938-0.

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36

Yang, Zhanwen, and Hermann Brunner. "Blow-up behavior of Hammerstein-type delay Volterra integral equations." Frontiers of Mathematics in China 8, no. 2 (March 4, 2013): 261–80. http://dx.doi.org/10.1007/s11464-013-0293-y.

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37

Bihun, Ya, and I. Skutar. "AVERAGING IN MULTIFREQUENCY SYSTEMS WITH DELAY AND LOCAL INTEGRAL CONDITIONS." Bukovinian Mathematical Journal 8, no. 2 (2020): 14–23. http://dx.doi.org/10.31861/bmj2020.02.02.

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Multifrequency systems of dierential equations were studied with the help of averaging method in the works by R.I. Arnold, Ye.O. Grebenikov, Yu.O. Mitropolsky, A.M. Samoilenko and many other scientists. The complexity of the study of such systems is their inherent resonant phenomena, which consist in the rational complete or almost complete commensurability of frequencies. As a result, the solution of the system of equations averaged over fast variables in the general case may deviate from the solution of the exact problem by the quantity O (1). The approach to the study of such systems, which was based on the estimation of the corresponding oscillating integrals, was proposed by A.M. Samoilenko, which allowed to obtain in the works by A.M. Samoilenko and R.I. Petryshyn a number of important results for multifrequency systems with initial , boundary and integral conditions. For multifrequency systems with an argument delay, the averaging method is substantiated in the works by Ya.Y. Bihun, R.I. Petryshyn, I.V. Krasnokutska and other authors. In this paper, the averaging method is used to study the solvability of a multifrequency system with an arbitrary nite number of linearly transformed arguments in slow and fast variables and integral conditions for slow and fast variables on parts of the interval [0, L] of the system of equations. An unimproved estimate of the error of the averaging method under the superimposed conditions is obtained, which clearly depends on the small parameter and the number of linearly transformed arguments in fast variables.
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38

Journal, Baghdad Science. "Solution of Variavle Delay integral eqiations using Variational approach." Baghdad Science Journal 3, no. 3 (September 3, 2006): 481–87. http://dx.doi.org/10.21123/bsj.3.3.481-487.

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The main objective of this research is to use the methods of calculus ???????? solving integral equations Altbataah When McCann slowdown is a function of time as the integral equation used in this research is a kind of Volterra
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39

Rihan, F. A., E. H. Doha, M. I. Hassan, and N. M. Kamel. "Numerical Treatments for Volterra Delay Integro-differential Equations." Computational Methods in Applied Mathematics 9, no. 3 (2009): 292–318. http://dx.doi.org/10.2478/cmam-2009-0018.

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AbstractThis paper presents a new technique for numerical treatments of Volterra delay integro-differential equations that have many applications in biological and physical sciences. The technique is based on the mono-implicit Runge — Kutta method for treating the differential part and the collocation method (using Boole’s quadrature rule) for treating the integral part. The efficiency and stability properties of this technique have been studied. Numerical results are presented to demonstrate the effectiveness of the methodology.
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40

FORYŚ, URSZULA. "BIOLOGICAL DELAY SYSTEMS AND THE MIKHAILOV CRITERION OF STABILITY." Journal of Biological Systems 12, no. 01 (March 2004): 45–60. http://dx.doi.org/10.1142/s0218339004001014.

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This paper deals with the stability analysis of biological delay systems. The Mikhailov criterion of stability is presented (and proved in the Appendix) for the case of discrete delay and distributed delay (i.e., delay in integral form). This criterion is used to check stability regions for some well-known equations, especially for the delay logistic equation and other equations with one discrete delay which appear in many applications. Some illustrations of the behavior of Mikhailov hodograph are shown.
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41

Usta, Fuat, and Mehmet Zeki Sarıkaya. "The analytical solution of Van der Pol and Lienard differential equations within conformable fractional operator by retarded integral inequalities." Demonstratio Mathematica 52, no. 1 (April 12, 2019): 204–12. http://dx.doi.org/10.1515/dema-2019-0017.

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AbstractIn this study we introduced and tested retarded conformable fractional integral inequalities utilizing non-integer order derivatives and integrals. In line with this purpose, we used the Katugampola type conformable fractional calculus which has several practical properties. These inequalities generalize some famous integral inequalities which provide explicit bounds on unknown functions. The results provided here had been implemented to the global existence of solutions to the conformable fractional differential equations with time delay.
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42

Caraballo, Tomás, P. E. Kloeden, and Pedro Marín-Rubio. "Numerical and finite delay approximations of attractors for logistic differential-integral equations with infinite delay." Discrete & Continuous Dynamical Systems - A 19, no. 1 (2007): 177–96. http://dx.doi.org/10.3934/dcds.2007.19.177.

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43

Cherevko, I. M., and A. B. Dorosh. "Boundary value problem solution existence for linear integro-differential equations with many delays." Carpathian Mathematical Publications 10, no. 1 (July 3, 2018): 65–70. http://dx.doi.org/10.15330/cmp.10.1.65-70.

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For the study of boundary value problems for delay differential equations, the contraction mapping principle and topological methods are used to obtain sufficient conditions for the existence of a solution of differential equations with a constant delay. In this paper, the ideas of the contraction mapping principle are used to obtain sufficient conditions for the existence of a solution of linear boundary value problems for integro-differential equations with many variable delays. Smoothness properties of the solutions of such equations are studied and the definition of the boundary value problem solution is proposed. Properties of the variable delays are analyzed and functional space is obtained in which the boundary value problem is equivalent to a special integral equation. Sufficient, simple for practical verification coefficient conditions for the original equation are found under which there exists a unique solution of the boundary value problem.
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44

Matsunaga, Hideaki, Satoru Murakami, Yutaka Nagabuchi, and Nguyen Van Minh. "Center Manifold Theorem and Stability for Integral Equations with Infinite Delay." Funkcialaj Ekvacioj 58, no. 1 (2015): 87–134. http://dx.doi.org/10.1619/fesi.58.87.

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45

Ding, Hui-Sheng, Ti-Jun Xiao, and Jin Liang. "Existence of positive almost automorphic solutions to nonlinear delay integral equations." Nonlinear Analysis: Theory, Methods & Applications 70, no. 6 (March 2009): 2216–31. http://dx.doi.org/10.1016/j.na.2008.03.001.

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46

Mao, Xuerong. "Existence and uniqueness of the solutions of delay stochastic integral equations." Stochastic Analysis and Applications 7, no. 1 (January 1989): 59–74. http://dx.doi.org/10.1080/07362998908809167.

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47

Burton, Theodore, and Ioannis Purnaras. "Global existence of solutions of integral equations with delay: progressive contractions." Electronic Journal of Qualitative Theory of Differential Equations, no. 49 (2017): 1–6. http://dx.doi.org/10.14232/ejqtde.2017.1.49.

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48

Zhang, C. J., and X. X. Liao. "Stability of BDF methods for nonlinear volterra integral equations with delay." Computers & Mathematics with Applications 43, no. 1-2 (January 2002): 95–102. http://dx.doi.org/10.1016/s0898-1221(01)00275-9.

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49

Karafyllis, Iasson, and Miroslav Krstic. "Stability of integral delay equations and stabilization of age-structured models." ESAIM: Control, Optimisation and Calculus of Variations 23, no. 4 (September 28, 2017): 1667–714. http://dx.doi.org/10.1051/cocv/2016069.

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50

Avaji, M., J. S. Hafshejani, S. S. Dehcheshme, and D. F. Ghahfarokh. "Solution of Delay Volterra Integral Equations Using the Variational Iteration Method." Journal of Applied Sciences 12, no. 2 (January 1, 2012): 196–200. http://dx.doi.org/10.3923/jas.2012.196.200.

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