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Relevant bibliographies by topics / Fractional order heat equation / Dissertations / Theses

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Dissertations / Theses on the topic 'Fractional order heat equation'

Author: Grafiati

Published: 5 June 2025

Last updated: 2 August 2025

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1

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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2

Farquhar, Megan Elizabeth. "Cardiac modelling with fractional calculus: An efficient computational framework for modelling the propagation of electrical impulses in the heart." Thesis, Queensland University of Technology, 2018. https://eprints.qut.edu.au/120682/1/__qut.edu.au_Documents_StaffHome_StaffGroupH%24_halla_Desktop_Megan_Farquhar_Thesis.pdf.

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Heart failure is one of the most common causes of death in the western world. Many heart problems are linked to disturbances in cardiac electrical activity. Further understanding of how electrical impulses propagate through the heart may lead to new diagnosis and treatment options. Using our novel numerical scheme, we are able to conduct preliminary investigations into the effect of fixed and variable order fractional Laplacian operators for modelling propagation of electrical impulses through the heart. We implement our numerical framework to solve the coupled monodomain, Beeler-Reuter mod

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3

COMI, GIULIA. "Two Fractional Stochastic Problems: Semi-Linear Heat Equation and Singular Volterra Equation." Doctoral thesis, Università degli studi di Pavia, 2019. http://hdl.handle.net/11571/1292026.

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4

Tyler, Jonathan. "Analysis and implementation of high-order compact finite difference schemes /." Diss., CLICK HERE for online access, 2007. http://contentdm.lib.byu.edu/ETD/image/etd2177.pdf.

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5

Tyler, Jonathan G. "Analysis and Implementation of High-Order Compact Finite Difference Schemes." BYU ScholarsArchive, 2007. https://scholarsarchive.byu.edu/etd/1278.

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The derivation of centered compact schemes at interior and boundary grid points is performed and an analysis of stability and computational efficiency is given. Compact schemes are high order implicit methods for numerical solutions of initial and/or boundary value problems modeled by differential equations. These schemes generally require smaller stencils than the traditional explicit finite difference counterparts. To avoid numerical instabilities at and near boundaries and in regions of mesh non-uniformity, a numerical filtering technique is employed. Experiments for non-stationary linear p

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6

Atwell, Jeanne A. "Proper Orthogonal Decomposition for Reduced Order Control of Partial Differential Equations." Diss., Virginia Tech, 2000. http://hdl.handle.net/10919/26985.

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Numerical models of PDE systems can involve very large matrix equations, but feedback controllers for these systems must be computable in real time to be implemented on physical systems. Classical control design methods produce controllers of the same order as the numerical models. Therefore, emph{reduced} order control design is vital for practical controllers. The main contribution of this research is a method of control order reduction that uses a newly developed low order basis. The low order basis is obtained by applying Proper Orthogonal Decomposition (POD) to a set of functional gains

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7

Talarcek, Steven C. "An Experimental Study of Disturbance Compensation and Control for a Fractional-Order System." University of Akron / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=akron1542303891784113.

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8

Abdelsheed, Ismail Gad Ameen. "Fractional calculus: numerical methods and SIR models." Doctoral thesis, Università degli studi di Padova, 2016. http://hdl.handle.net/11577/3422267.

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Fractional calculus is ”the theory of integrals and derivatives of arbitrary order, which unify and generalize the notions of integer-order differentiation and n-fold integration”. The idea of generalizing differential operators to a non-integer order, in particular to the order 1/2, first appears in the correspondence of Leibniz with L’Hopital (1695), Johann Bernoulli (1695), and John Wallis (1697) as a mere question or maybe even play of thoughts. In the following three hundred years a lot of mathematicians contributed to the fractional calculus: Laplace (1812), Lacroix (1812), Fourier (1822

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9

Hejazi, Hala Ahmad. "Finite volume methods for simulating anomalous transport." Thesis, Queensland University of Technology, 2015. https://eprints.qut.edu.au/81751/1/Hala%20Ahmad_Hejazi_Thesis.pdf.

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In this thesis a new approach for solving a certain class of anomalous diffusion equations was developed. The theory and algorithms arising from this work will pave the way for more efficient and more accurate solutions of these equations, with applications to science, health and industry. The method of finite volumes was applied to discretise the spatial derivatives, and this was shown to outperform existing methods in several key respects. The stability and convergence of the new method were rigorously established.

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10

Badía, José M., Peter Benner, Rafael Mayo, Enrique S. Quintana-Ortí, Gregorio Quintana-Ortí, and Jens Saak. "Parallel Order Reduction via Balanced Truncation for Optimal Cooling of Steel Profiles." Universitätsbibliothek Chemnitz, 2006. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200601566.

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We employ two efficient parallel approaches to reduce a model arising from a semi-discretization of a controlled heat transfer process for optimal cooling of a steel profile. Both algorithms are based on balanced truncation but differ in the numerical method that is used to solve two dual generalized Lyapunov equations, which is the major computational task. Experimental results on a cluster of Intel Xeon processors compare the efficacy of the parallel model reduction algorithms.

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11

Han, Cundi. "Numerical method for non-integer order PDE : approximations and parameter identification." Electronic Thesis or Diss., Bourges, INSA Centre Val de Loire, 2024. http://www.theses.fr/2024ISAB0004.

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L'objectif principal de cette thèse est de proposer une méthode numérique basée sur les polynômes de Bernstein et des termes de sinusoidaux. Cette méthode est utilisée pour traiter numériquement les modèles structurels linéaires et non linéaires avec dérivée d'ordre fractionnaire. Comparé à l'ordre entier, l'ordre fractionnaire offre une meilleure mémoire temporelle et permet d'utiliser moins de paramètres pour simuler plus précisément le comportement dynamique du modèle. Cependant, il est très difficile d'obtenir la solution analytique du modèle structurel en raison de l'existence de l'ordre

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12

Pesee, Chatchai. "Stochastic modelling of financial processes with memory and semi-heavy tails." Thesis, Queensland University of Technology, 2005. https://eprints.qut.edu.au/16057/2/Chatchai%20Pesee%20Thesis.pdf.

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This PhD thesis aims to study financial processes which have semi-heavy-tailed marginal distributions and may exhibit memory. The traditional Black-Scholes model is expanded to incorporate memory via an integral operator, resulting in a class of market models which still preserve the completeness and arbitragefree conditions needed for replication of contingent claims. This approach is used to estimate the implied volatility of the resulting model. The first part of the thesis investigates the semi-heavy-tailed behaviour of financial processes. We treat these processes as continuous-t

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13

Pesee, Chatchai. "Stochastic Modelling of Financial Processes with Memory and Semi-Heavy Tails." Queensland University of Technology, 2005. http://eprints.qut.edu.au/16057/.

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This PhD thesis aims to study financial processes which have semi-heavy-tailed marginal distributions and may exhibit memory. The traditional Black-Scholes model is expanded to incorporate memory via an integral operator, resulting in a class of market models which still preserve the completeness and arbitragefree conditions needed for replication of contingent claims. This approach is used to estimate the implied volatility of the resulting model. The first part of the thesis investigates the semi-heavy-tailed behaviour of financial processes. We treat these processes as continuous-t

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14

Schaeffer, Nicolas. "Étude d'équations aux dérivées partielles dirigées par une perturbation stochastique." Electronic Thesis or Diss., Université de Lorraine, 2022. http://www.theses.fr/2022LORR0054.

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Le sujet de cette thèse porte sur l'étude de certaines équations aux dérivées partielles non linéaires et dirigées par une perturbation aléatoire. Au Chapitre 1, on définit la notion de bruit blanc et de bruit fractionnaire. On décrit ensuite la procédure générale permettant de prouver le caractère bien posé des modèles considérés. Après avoir présenté un état de l'art, on détaille et commente les différents résultats obtenus en insistant sur les nouveautés et en précisant les éventuelles perspectives. Au Chapitre 2, on présente les outils probabilistes dont on aura besoin tout au long de notr

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15

(9216107), Jordan D. F. Petty. "Modeling a Dynamic System Using Fractional Order Calculus." Thesis, 2020.

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<p>Fractional calculus is the integration and differentiation to an arbitrary or fractional order. The techniques of fractional calculus are not commonly taught in engineering curricula since physical laws are expressed in integer order notation. Dr. Richard Magin (2006) notes how engineers occasionally encounter dynamic systems in which the integer order methods do not properly model the physical characteristics and lead to numerous mathematical operations. In the following study, the application of fractional order calculus to approximate the angular position of the disk oscillating in a New

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16

WU, JI-FENG, and 吳吉峰. "An application of fractional calculus to a partial differential equation of the second order." Thesis, 1989. http://ndltd.ncl.edu.tw/handle/84725545352008921259.

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17

SARV, AHRABI SIMA. "Fractional model of cancer immunotherapy and its optimal control." Doctoral thesis, 2018. http://hdl.handle.net/11573/1185669.

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Cancer is one of the most serious illnesses in all of the world. Although most of the cancer patients are treated with chemotherapy, radiotherapy and surgery, wide research is conducted related to experimental and theoretical immunology. In recent years, the research on cancer immunotherapy has led to major medical advances. Cancer immunotherapy refers to the stimulation of immune system to deal with cancer cells. In medical practice, it is mainly achieved by using effector cells such as activated T-cells and Interleukin-2 (IL-2), which is the main cytokine responsible for lymphocyte activati

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18

Toudjeu, Ignace Tchangou. "Mathematical analysis of generalized linear evolution equations with the non-singular kernel derivative." Diss., 2019. http://hdl.handle.net/10500/25774.

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Linear Evolution Equations (LEE) have been studied extensively over many years. Their extension in the field of fractional calculus have been defined by Dαu(x, t) = Au(x, t), where α is the fractional order and Dα is a generalized differential operator. Two types of generalized differential operators were applied to the LEE in the state-of-the-art, producing the Riemann-Liouville and the Caputo time fractional evolution equations. However the extension of the new Caputo-Fabrizio derivative (CFFD) to these equations has not been developed. This work investigates existing fractional derivative

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