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Dissertations / Theses on the topic 'Impulsive fractional differential equations'

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Published: 2 June 2025

Last updated: 31 July 2025

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1

Zhu, Wei. "Fractional differential equations in risk theory." Thesis, University of Liverpool, 2018. http://livrepository.liverpool.ac.uk/3018514/.

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This thesis considers one of the central topics in the actuarial mathematics literature, deriving the probability of ruin in the collective risk model. The classical risk model and renewal risk models are focused in this project, where the claim number processes are assumed to be Poisson counting processes and any general renewal counting processes, respectively. The first part of this project is about the classical risk model. We look at the case when claim sizes follow a gamma distribution. Explicit expressions for ruin probabilities are derived via Laplace transform and inverse Laplace tran

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2

Ozbekler, Abdullah. "Sturm Comparison Theory For Impulsive Differential Equations." Phd thesis, METU, 2005. http://etd.lib.metu.edu.tr/upload/3/12606894/index.pdf.

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In this thesis, we investigate Sturmian comparison theory and oscillation for second order impulsive differential equations with fixed moments of impulse actions. It is shown that impulse actions may greatly alter the oscillation behavior of solutions. In chapter two, besides Sturmian type comparison results, we give Leightonian type comparison theorems and obtain Wirtinger type inequalities for linear, half-linear and non-selfadjoint equations. We present analogous results for forced super linear and super half-linear equations with damping. In chapter three, we derive suf

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3

Ballinger, George Henri. "Qualitative theory of impulsive delay differential equations." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp03/NQ51178.pdf.

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4

Tapdigoglu, Ramiz. "Inverse problems for fractional order differential equations." Thesis, La Rochelle, 2019. http://www.theses.fr/2019LAROS004/document.

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Dans cette thèse, nous nous intéressons à résoudre certains problèmes inverses pour des équations différentielles aux dérivées fractionnaires. Un problème inverse est généralement mal posé. Un problème mal posé est un problème qui ne répond pas à l’un des trois critères de Hadamard pour être bien posé, c’est-à-dire, soit l’existence, l’unicité ou une dépendance continue aux données n'est plus vraie, à savoir, des petits changements dans les données de mesure entraînent des changements indéfiniment importants dans la solution. La plupart des difficultés à résoudre des problèmes mal posés sont c

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5

Miron, Rachelle. "Impulsive Differential Equations with Applications to Infectious Diseases." Thèse, Université d'Ottawa / University of Ottawa, 2014. http://hdl.handle.net/10393/30948.

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Impulsive differential equations are useful for modelling certain biological events. We present three biological applications showing the use of impulsive differential equations in real-world problems. We also look at the effects of stability on a reduced two-dimensional impulsive HIV system. The first application is a system describing HIV induction-maintenance therapy, which shows how the solution to an impulsive system is used in order to find biological results (adherence, etc). A second application is an HIV system describing the interaction between T-cells, virus and drugs. Stability

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6

Lin, Xue Lei. "Separable preconditioner for time-space fractional diffusion equations." Thesis, University of Macau, 2017. http://umaclib3.umac.mo/record=b3691377.

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7

Smith, Robert. "Impulsive differential equations with applications to self-cycling fermentation /." *McMaster only, 2001.

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8

Wei, Hui Qin. "Preconditioners for solving fractional diffusion equations with discontinuous coefficients." Thesis, University of Macau, 2017. http://umaclib3.umac.mo/record=b3691375.

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9

Connolly, Joseph Arthur. "The numerical solution of fractional and distributed order differential equations." Thesis, University of Chester, 2004. http://hdl.handle.net/10034/76687.

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Fractional Calculus can be thought of as a generalisation of conventional calculus in the sense that it extends the concept of a derivative (integral) to include non-integer orders. Effective mathematical modelling using Fractional Differential Equations (FDEs) requires the development of reliable flexible numerical methods. The thesis begins by reviewing a selection of numerical methods for the solution of Single-term and Multi-term FDEs. We then present: 1. a graphical technique for comparing the efficiency of numerical methods. We use this to compare Single-term and Multi-term methods and g

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10

Pal, Kamal K. "Higher order numerical methods for fractional order differential equations." Thesis, University of Chester, 2015. http://hdl.handle.net/10034/613354.

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11

Simpson, Arthur Charles. "Numerical methods for the solution of fractional differential equations." Thesis, University of Liverpool, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.250281.

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The fractional calculus is a generalisation of the calculus of Newton and Leibniz. The substitution of fractional differential operators in ordinary differential equations substantially increases their modelling power. Fractional differential operators set exciting new challenges to the computational mathematician because the computational cost of approximating fractional differential operators is of a much higher order than that necessary for approximating the operators of classical calculus. 1. We present a new formulation of the fractional integral. 2. We use this to develop a new method fo

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12

Sambandham, Bhuvaneswari. "Analysis of Sequential Caputo Fractional Differential Equations with Applications." Thesis, University of Louisiana at Lafayette, 2016. http://pqdtopen.proquest.com/#viewpdf?dispub=10163318.

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<p> The solution for sequential Caputo linear fractional differential equations with variable coefficients of order q, 0 < q < 1 can be obtained from symbolic representation form. Since the iterative method developed in Chapter 2 is time-consuming even for the simple linear fractional differential equations with variable coefficients, the direct numerical approximation developed in Chapter 3 is very useful tool when computing the linear and non-linear fractional differential equations of a specific type. This direct numerical method is useful in developing the monotone method and the qua

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13

Guo, Xu. "Fractional differential equations for modelling financial processes with jumps." HKBU Institutional Repository, 2015. https://repository.hkbu.edu.hk/etd_oa/192.

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The standard Black-Scholes model is under the assumption of geometric Brownian motion, and the log-returns for Black-Scholes model are independent and Gaussian. However, most of the recent literature on the statistical properties of the log-returns makes this hypothesis not always consistent. One of the ongoing research topics is to nd a better nancial pricing model instead of the Black-Scholes model. In the present work, we concentrate on two typical 1-D option pricing models under the general exponential L evy processes, namely the nite moment log-stable (FMLS) model and the the Carr-Gema

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14

Ugur, Omur. "Boundary Value Problems For Higher Order Linear Impulsive Differential Equations." Phd thesis, METU, 2003. http://etd.lib.metu.edu.tr/upload/686691/index.pdf.

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_I The theory of impulsive di&reg<br>erential equations has become an important area of research in recent years. Linear equations, meanwhile, are fundamental in most branches of applied mathematics, science, and technology. The theory of higher order linear impulsive equations, however, has not been studied as much as the cor- responding theory of ordinary di&reg<br>erential equations. In this work, higher order linear impulsive equations at &macr<br>xed moments of impulses together with certain boundary conditions are investigated by making use of a Green&#039<br>s formula, constructed for p

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15

Alzabut, Jehad. "Periodic Solutions And Stability Of Linear Impulsive Delay Differential Equations." Phd thesis, METU, 2004. http://etd.lib.metu.edu.tr/upload/2/12604901/index.pdf.

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In this thesis, we investigate impulsive differential systems with delays of the form And more generally of the form The dissertation consists of five chapters. The first chapter serves as introduction, contains preliminary considerations and assertions that will be encountered in the sequel. In chapter 2, we construct the adjoint systems and obtain the variation of parameters formulas of the solutions in terms of fundamental matrices. The asymptotic behavior of solutions of systems satisfying the Perron co

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16

Yuan, Huifang. "Spectral collocation methods for the fractional PDEs in unbounded domain." HKBU Institutional Repository, 2018. https://repository.hkbu.edu.hk/etd_oa/558.

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This thesis is concerned with a particular numerical approach for solving the fractional partial differential equations (PDEs). In the last two decades, it has been observed that many practical systems are more accurately described by fractional differential equations (FDEs) rather than the traditional differential equation approaches. Consequently, it has become an important research area to study the theoretical and numerical aspects of various types of FDEs. This thesis will explore high order numerical methods for solving FDEs numerically. More precisely, spectral methods which exhibits ex

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17

Ferrás, Luís J. L. "Numerical solution of fractional differential equations and their application to physics and engineering." Thesis, University of Chester, 2018. http://hdl.handle.net/10034/621788.

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This dissertation presents new numerical methods for the solution of fractional differential equations of single and distributed order that find application in the different fields of physics and engineering. We start by presenting the relationship between fractional derivatives and processes like anomalous diffusion, and, we then develop new numerical methods for the solution of the time-fractional diffusion equations. The first numerical method is developed for the solution of the fractional diffusion equations with Neumann boundary conditions and the diffusivity parameter depending on the s

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18

Nie, Tianyang. "Stochastic differential equations with constraints on the state : backward stochastic differential equations, variational inequalities and fractional viability." Thesis, Brest, 2012. http://www.theses.fr/2012BRES0047.

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Le travail de thèse est composé de trois thèmes principaux : le premier étudie l'existence et l'unicité pour des équations différentielles stochastiques (EDS) progressives-rétrogrades fortement couplées avec des opérateurs sous-différentiels dans les deux équations, dans l’équation progressive ainsi que l’équation rétrograde, et il discute également un nouveau type des inégalités variationnelles partielles paraboliques associées, avec deux opérateurs sous-différentiels, l’un agissant sur le domaine de l’état, l’autre sur le co-domaine. Le second thème est celui des EDS rétrogrades sans ainsi q

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19

Kumar, Pankaj. "New numerical schemes for the solution of fractional differential equations /." Available to subscribers only, 2006. http://proquest.umi.com/pqdweb?did=1240704821&sid=2&Fmt=2&clientId=1509&RQT=309&VName=PQD.

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Thesis (M.S.)--Southern Illinois University Carbondale, 2006.<br>"Department of Mechanical Engineering and Energy Processes." Includes bibliographical references (leaves 98-106). Also available online.

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20

Neuenkirch, Andreas. "Optimal approximation of stochastic differential equations with additive fractional noise /." Aachen : Shaker, 2006. http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&doc_number=015005376&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA.

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21

Nguyen, Cu Ngoc. "Stochastic differential equations with long-memory input." Thesis, Queensland University of Technology, 2001.

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22

Shi, Chen Yang. "High order compact schemes for fractional differential equations with mixed derivatives." Thesis, University of Macau, 2017. http://umaclib3.umac.mo/record=b3691348.

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23

Weilbeer, Marc. "Efficient numerical methods for fractional differential equations and their analytical background." [S.l.] : [s.n.], 2005. http://www.digibib.tu-bs.de/?docid=00004372.

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24

Deng, Si Wen. "Precondition technique for conservative space-fractional diffusion equations in convex domains." Thesis, University of Macau, 2018. http://umaclib3.umac.mo/record=b3950597.

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25

Wilathgamuwa, Don Gayan. "STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS DRIVEN BY FRACTIONAL BROWNIAN MOTION AND THEIR GENERALIZATIONS." OpenSIUC, 2012. https://opensiuc.lib.siu.edu/dissertations/513.

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We consider a stochastic functional differential equation with infinite memory driven by a fractional Brownian motion with Hurst parameter $H>1/2$. We prove an existence and uniqueness result of the solution to the stochastic differential equation. We investigate the dependence of the solution on the initial condition and the existence of finite moments of the solution. Furthermore we generalize these results to wider classes of stochastic differential equations. The stochastic integral with respect to fractional Brownian motion is defined as a pathwise Riemann-Stieltjes integral.

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26

Almusharrf, Amera. "Development of Fractional Trigonometry and an Application of Fractional Calculus to Pharmacokinetic Model." TopSCHOLAR®, 2011. http://digitalcommons.wku.edu/theses/1048.

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27

Lenz, Simon Manfred [Verfasser], and Hans Georg [Akademischer Betreuer] Bock. "Impulsive Hybrid Discrete-Continuous Delay Differential Equations / Simon Manfred Lenz ; Betreuer: Hans Georg Bock." Heidelberg : Universitätsbibliothek Heidelberg, 2014. http://d-nb.info/1179925408/34.

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28

Lenz, Simon M. [Verfasser], and Hans Georg [Akademischer Betreuer] Bock. "Impulsive Hybrid Discrete-Continuous Delay Differential Equations / Simon Manfred Lenz ; Betreuer: Hans Georg Bock." Heidelberg : Universitätsbibliothek Heidelberg, 2014. http://nbn-resolving.de/urn:nbn:de:bsz:16-heidok-171173.

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29

Carella, Alfredo Raúl. "Spectral Finite Element Methods for solving Fractional Differential Equations with applications in Anomalous Transport." Doctoral thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for energi- og prosessteknikk, 2012. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-17656.

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Quantifying species transport rates is a main concern in chemical and petrochemical industries. In particular, the design and operation of many large-scale industrial chemical processes is as much dependent on diffusion as it is on reaction rates. However, the existing diffusion models sometimes fail to predict experimentally observed behaviors and their accuracy is usually insufficient for process optimization purposes. Fractional diffusion models offer multiple possibilities for generalizing Fick’s law in a consistent manner in order to account for history dependence and nonlocal effects. Th

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30

Neto, Paulo Mendes de Carvalho. "Fractional differential equations: a novel study of local and global solutions in Banach spaces." Universidade de São Paulo, 2013. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-06062013-145531/.

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Motivated by the huge success of the applications of the abstract fractional equations in many areas of science and engineering, and by the unsolved question in this theory, in this work we study several matters related to abstract fractional Cauchy problems of order \'alpha\' \'it belongs\' (0, 1). We search to answer some questions that were open: for instance, we analyze the existence of local mild solutions for the problem, and its possible continuation to a maximal interval of existence. The case of critical nonlinearities and corresponding regular mild solutions is also studied. Finally,

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31

Agarwal, Divyanshu. "A Study on the Feasibility of Using Fractional Differential Equations for Roll Damping Models." Thesis, Virginia Tech, 2015. http://hdl.handle.net/10919/52959.

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An optimization algorithm has been developed to study the effectiveness of substituting time tested ODEs with FDEs as applied to ship motions, specifically with an eye toward modeling different forms of roll damping. Relations between the order of differentiation a and damping coefficient b in the FDEs have been drawn for changing damping, added moment of inertia, and initial roll angle. A pitch model has also been studied and compared to the roll model. The error at each of these a and b pairs has also been calculated using an L2-norm. An initial effort was made to correlate the FDE coefficie

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32

Er, Aynur. "Stability of Linear Difference Systems in Discrete and Fractional Calculus." TopSCHOLAR®, 2017. http://digitalcommons.wku.edu/theses/1946.

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The main purpose of this thesis is to define the stability of a system of linear difference equations of the form, ∇y(t) = Ay(t), and to analyze the stability theory for such a system using the eigenvalues of the corresponding matrix A in nabla discrete calculus and nabla fractional discrete calculus. Discrete exponential functions and the Putzer algorithms are studied to examine the stability theorem. This thesis consists of five chapters and is organized as follows. In the first chapter, the Gamma function and its properties are studied. Additionally, basic definitions, properties and some m

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33

Muniswamy, Sowmya. "Analytical and Numerical Approach to Caputo Fractional Differential Equations via Generalized Iterative Schemes with Applications." Thesis, University of Louisiana at Lafayette, 2014. http://pqdtopen.proquest.com/#viewpdf?dispub=3622948.

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<p> Natural lower and upper solutions for initial value problems guarantees the interval of existence. However, coupled lower and upper solutions used as initial approximation in generalized iterative method are very useful since the iterates can be computed without any extra assumption. Generalized monotone method, along with the method of lower and upper solutions, has been used to develop the coupled lower and upper solutions on an extended interval for both scalar and system of Caputo fractional differential equations. This method yields linear convergence. Generalized quasilinearization m

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34

Valente, Maria Serra. "Stability of non-trivial solutions of stochastic differential equations driven by the fractional Brownian motion." Master's thesis, Instituto Superior de Economia e Gestão, 2019. http://hdl.handle.net/10400.5/18993.

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Mestrado em Mathematical Finance<br>O objectivo desta dissertação é o de generalizar um resultado sobre a estabilidade exponencial de soluções triviais de equações diferenciais estocásticas com movimento Browniano fraccionário, desenvolvido por Garrido-Atienza et al., para soluções não-triviais. São apresentadas noções de cálculo fraccionário, assim como a definição e principias propriedades do movimento Browniano fraccionário. De seguida, um framework para equações diferenciais estocásticas com movimento Browniano fraccionário é definido juntamente com resultados de existência e unicidade de

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35

Banks, Nicola E. "Insights from the parallel implementation of efficient algorithms for the fractional calculus." Thesis, University of Chester, 2015. http://hdl.handle.net/10034/613841.

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This thesis concerns the development of parallel algorithms to solve fractional differential equations using a numerical approach. The methodology adopted is to adapt existing numerical schemes and to develop prototype parallel programs using the MatLab Parallel Computing Toolbox (MPCT). The approach is to build on existing insights from parallel implementation of ordinary differential equations methods and to test a range of potential candidates for parallel implementation in the fractional case. As a consequence of the work, new insights on the use of MPCT for prototyping are presented, alon

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36

McVinish, Ross Stewart. "Stochastic analysis and approximation of fractional diffusion." Thesis, Queensland University of Technology, 2002.

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37

Church, Kevin. "Applications of Impulsive Differential Equations to the Control of Malaria Outbreaks and Introduction to Impulse Extension Equations: a General Framework to Study the Validity of Ordinary Differential Equation Models with Discontinuities in State." Thesis, Université d'Ottawa / University of Ottawa, 2014. http://hdl.handle.net/10393/31874.

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Impulsive differential equations are often used in mathematical modelling to simplify complicated hybrid models. We propose an inverse framework inspired by impulsive differential equations, called impulse extension equations, which can be used as a tool to determine when these impulsive models are accurate. The linear theory is the primary focus, for which theorems analoguous to ordinary and impulsive differential equations are derived. Results explicitly connecting the stability of impulsive differential equations to related impulse extension equations are proven in what we call time scale c

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38

Rodrigues, Fabio Grangeiro 1980. "Sobre cálculo fracionário e soluções da equação de Bessel." [s.n.], 2015. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306992.

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Orientador: Edmundo Capelas de Oliveira<br>Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica<br>Made available in DSpace on 2018-08-26T23:00:41Z (GMT). No. of bitstreams: 1 Rodrigues_FabioGrangeiro_D.pdf: 1185818 bytes, checksum: 96f82c6ff4622e4ecdd3ccae79803dae (MD5) Previous issue date: 2015<br>Resumo: Neste trabalho é apresentado um modo de se obter soluções de um caso particular da equação hipergeométrica confluente, a equação de Bessel de ordem p, utilizando-se da teoria do cálculo de ordem arbitrária, também conhecido pop

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39

Hernández-Hernández, Ma Elena. "On the probabilistic approach to the solution of generalized fractional differential equations of Caputo and Riemann-Liouville type." Thesis, University of Warwick, 2016. http://wrap.warwick.ac.uk/88783/.

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This dissertation focuses on the study of generalized fractional differential equations involving a general class of non-local operators which are referred to as the generalized fractional derivatives of Caputo and Riemann-Liouville (RL) type. These operators were introduced recently as a probabilistic extension of the classical fractional Caputo and Riemann-Liouville derivatives of order β ε (0,1) (when acting on regular enough functions). The main contribution of this work lies in displaying the use of stochastic analysis as a valuable approach for the study of fractional differential equati

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40

Melichov, Dmitrij. "On estimation of the Hurst index of solutions of stochastic differential equations." Doctoral thesis, Lithuanian Academic Libraries Network (LABT), 2011. http://vddb.laba.lt/obj/LT-eLABa-0001:E.02~2011~D_20111228_165042-00002.

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The main topic of this dissertation is the estimation of the Hurst index H of the solutions of stochastic differential equations (SDEs) driven by the fractional Brownian motion (fBm). Firstly, the limit behavior of the first and second order quadratic variations of the solutions of SDEs driven by the fBm is analyzed. This yields several strongly consistent estimators of the Hurst index H. Secondly, it is proved that in case the solution of the SDE is replaced by its Milstein approximation, the estimators remain strongly consistent. Additionally, the possibilities of applying the increment ra

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41

Charoenphon, Sutthirut. "Green's Functions of Discrete Fractional Calculus Boundary Value Problems and an Application of Discrete Fractional Calculus to a Pharmacokinetic Model." TopSCHOLAR®, 2014. http://digitalcommons.wku.edu/theses/1327.

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Fractional calculus has been used as a research tool in the fields of pharmacology, biology, chemistry, and other areas [3]. The main purpose of this thesis is to calculate Green's functions of fractional difference equations, and to model problems in pharmacokinetics. We claim that the discrete fractional calculus yields the best prediction performance compared to the continuous fractional calculus in the application of a one-compartmental model of drug concentration. In Chapter 1, the Gamma function and its properties are discussed to establish a theoretical basis. Additionally, the basics o

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42

Godoy, Jaqueline Bezerra. "Método da média para equações diferenciais funcionais retardadas impulsivas via equações diferenciais generalizadas." Universidade de São Paulo, 2009. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-10052010-085321/.

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Neste trabalho, nós consideramos o seguinte problema de valor inicial para uma equação diferencial funcional retardada com impulsos { \'x PONTO\' = \'varepsilon\' f (t, \'x IND.t\'), t \' DIFERENTE\' \'t IND. k\', \'DELTA\' x(\'t IND. k\') = \'varepsilon\' \' I IND. k\' (x ( \'t IND.k\')), k = 0, 1, 2, ... \'x IND. t IND.0\' = \' phi\', onde f está definida em um aberto \' OMEGA\' de R x \' G POT. -\' ([- r, 0], \' R POT. n\') e assume valores em \'R POT. n\', \' \'varepsilon\' \'G POT. - ([ - r, 0], \'R POT.n\'), r .0, onde \' G POT -\' ([ - r, 0], \' R POT. n\') denota o espaço das funçõe

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43

Ellery, Adam J. "Modelling transport through biological environments that contain obstacles." Thesis, Queensland University of Technology, 2017. https://eprints.qut.edu.au/106798/1/Adam_Ellery_Thesis.pdf.

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Transport through biological environments that are densely crowded with obstacles is often classified as anomalous, rather than Fickian diffusion. Researchers often describe these transport processes using either a random walk model or a fractional order differential equation model. To explore these ideas, we simulate transport through a crowded environment that is populated by impenetrable immobile obstacles. Our work suggests that it may be inappropriate to model transport through a crowded environment using these standard approaches. We develop a new analytical method for modelling the t

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44

Santos, Matheus Correia dos 1987. "Elliptic equations with nonlinear gradient terms and fractional diffusion equations = Equações elípticas com termos gradientes não lineares e equações de difusão fracionárias." [s.n.], 2015. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307599.

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Orientadores: Lucas Catão de Freitas Ferreira, Marcelo da Silva Montenegro, José Antonio Carrillo de la Plata<br>Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica<br>Made available in DSpace on 2018-08-26T15:13:15Z (GMT). No. of bitstreams: 1 Santos_MatheusCorreiados_D.pdf: 865476 bytes, checksum: 31a8b558231b701d81c20bf2712e4f50 (MD5) Previous issue date: 2015<br>Resumo: Analisaremos dois problemas neste trabalho. Na primeira parte, estudaremos a existência de soluções para uma equação elíptica semilinear no espaço euclidiano

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45

Kisela, Tomáš. "Zlomkové diferenciální rovnice a jejich aplikace." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2008. http://www.nusl.cz/ntk/nusl-227885.

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Zlomkový kalkulus je matematická disciplína zabývající se vlastnostmi derivací a integrálů neceločíselných řádů (nazývaných zlomkové derivace a integrály, zkráceně diferintegrály) a metodami řešení diferenciálních rovnic obsahujících zlomkové derivace neznámé funkce (tzv. zlomkovými diferenciálními rovnicemi). V této práci představujeme standardní přístupy k definicím zlomkového kalkulu a důkazy některých základních vlastností diferintegrálů. Dále uvádíme krátký přehled metod řešení některých lineárních zlomkových diferenciálních rovnic a vymezujeme hranice jejich použitelnosti. Na závěr si vš

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46

Haress, El Mehdi. "Numerical approximation and long-time behaviour of some singular stochastic (partial) differential equations." Electronic Thesis or Diss., université Paris-Saclay, 2024. http://www.theses.fr/2024UPASM038.

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On explore l'approximation numérique et le comportement en temps long de certaines équations stochastiques dirigées par des termes de dérive dissipatifs et/ou distributionnels.Premièrement, les équations différentielles stochastiques (EDS) avec un mouvement brownien fractionnaire (mBf) et une dérive distributionnelle sont étudiées. La convergence d'un schéma d'Euler modéré est quantifiée. Des techniques similaires sont appliquées à l'équation de la chaleur stochastique (SHE) avec un bruit blanc spatio-temporel et un terme de réaction distributionnel, et les mêmes résultats sont obtenus pour un

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Contharteze, Eliana 1984. "Equações diferenciais fracionárias e as funções de Mittag-Leffler." [s.n.], 2014. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306993.

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Orientador: Edmundo Capelas de Oliveira<br>Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica<br>Made available in DSpace on 2018-08-26T02:22:44Z (GMT). No. of bitstreams: 1 Contharteze_Eliana_D.pdf: 2292843 bytes, checksum: c606ccefade98acff6e3f2b74c2ac021 (MD5) Previous issue date: 2014<br>Resumo: Apresentamos operadores de integração e derivação fracionárias, que em particular, podem ser utilizados para descrever um processo difusivo anômalo através de uma equação diferencial fracionária. Como aplicação, discutimos uma equaçã

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Nersesov, Sergey G. "Nonlinear Impulsive and Hybrid Dynamical Systems." Diss., Georgia Institute of Technology, 2005. http://hdl.handle.net/1853/7147.

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Modern complex dynamical systems typically possess a multiechelon hierarchical hybrid structure characterized by continuous-time dynamics at the lower-level units and logical decision-making units at the higher-level of hierarchy. Hybrid dynamical systems involve an interacting countable collection of dynamical systems defined on subregions of the partitioned state space. Thus, in addition to traditional control systems, hybrid control systems involve supervising controllers which serve to coordinate the (sometimes competing) actions of the lower-level controllers. A subclass of hybrid dynamic

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Fernandez, Arran. "Analysis in fractional calculus and asymptotics related to zeta functions." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/284390.

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This thesis presents results in two apparently disparate mathematical fields which can both be examined -- and even united -- by means of pure analysis. Fractional calculus is the study of differentiation and integration to non-integer orders. Dating back to Leibniz, this idea was considered by many great mathematical figures, and in recent decades it has been used to model many real-world systems and processes, but a full development of the mathematical theory remains incomplete. Many techniques for partial differential equations (PDEs) can be extended to fractional PDEs too. Three chapters b

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McKenzie, Lauren Clara Browning. "The Effects of Adherence to Antiretroviral Therapy for HIV-1 Infection." Thesis, Université d'Ottawa / University of Ottawa, 2021. http://hdl.handle.net/10393/42202.

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The emergence of drug resistance is a serious threat to the long-term virologic success and durability of HIV-1 therapy. Adherence has been shown to be a major determinant of drug resistance; however, each pharmacologic class of antiretroviral drugs has a unique adherence–resistance relationship. We develop an immunological model of the HIV-1 infected human immune system that integrates the unique mechanisms of action of reverse transcriptase and protease inhibiting drugs. A system of impulsive differential equations is used to examine the drug kinetics within CD4⁺ T cells. Stability analysis

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