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Dissertations / Theses on the topic 'Fractional calculus'

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Published: 4 June 2021

Last updated: 25 July 2025

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1

Tavares, Dina dos Santos. "Fractional calculus of variations." Doctoral thesis, Universidade de Aveiro, 2017. http://hdl.handle.net/10773/22184.

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Doutoramento em Matemática e Aplicações<br>O cálculo de ordem não inteira, mais conhecido por cálculo fracionário, consiste numa generalização do cálculo integral e diferencial de ordem inteira. Esta tese é dedicada ao estudo de operadores fracionários com ordem variável e problemas variacionais específicos, envolvendo também operadores de ordem variável. Apresentamos uma nova ferramenta numérica para resolver equações diferenciais envolvendo derivadas de Caputo de ordem fracionária variável. Consideram- -se três operadores fracionários do tipo Caputo, e para cada um deles é apresentad

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2

Kimeu, Joseph M. "Fractional Calculus: Definitions and Applications." TopSCHOLAR®, 2009. http://digitalcommons.wku.edu/theses/115.

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3

McBride, Adam C. "Fractional calculus, fractional powers of operators and Mellin multiplier transforms." Thesis, University of Edinburgh, 1994. http://hdl.handle.net/1842/15310.

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We shall present a theory of fractional calculus for generalised functions on (0,∞) and use this theory as a basis for extensions to some related areas. In the first section, appropriate spaces of test-functions and generalised functions on (0,∞) are introduced and the properties of operators of fractional calculus obtained relative to these spaces. Applications are given to hypergeometric integral equations, Hankel transforms and dual integral equations of Titchmarsh type. In the second section, the Mellin transform is used to define fractional powers of a very general class of operators. The

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4

Ferreira, Rui Alexandre Cardoso. "Calculus of variations on time scales and discrete fractional calculus." Doctoral thesis, Universidade de Aveiro, 2010. http://hdl.handle.net/10773/2921.

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Doutoramento em Matemática<br>Estudamos problemas do cálculo das variações e controlo óptimo no contexto das escalas temporais. Especificamente, obtemos condições necessárias de optimalidade do tipo de Euler–Lagrange tanto para lagrangianos dependendo de derivadas delta de ordem superior como para problemas isoperimétricos. Desenvolvemos também alguns métodos directos que permitem resolver determinadas classes de problemas variacionais através de desigualdades em escalas temporais. No último capítulo apresentamos operadores de diferença fraccionários e propomos um novo cálculo das variações fr

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5

Ito, Yu. "Rough path theory via fractional calculus." 京都大学 (Kyoto University), 2015. http://hdl.handle.net/2433/199445.

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6

Waddell, Chris. "Fractional calculus and scales of spaces." Thesis, University of Strathclyde, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.288637.

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7

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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8

Shen, Xin. "Applications of Fractional Calculus In Chemical Engineering." Thesis, Université d'Ottawa / University of Ottawa, 2018. http://hdl.handle.net/10393/37577.

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Fractional calculus, which is a generalization of classical calculus, has been the subject of numerous applications in physics and engineering during the last decade. In this thesis, fractional calculus has been implemented for chemical engineering applications, namely in process control and in the modeling mass transfer in adsorption. With respect to process control, some researchers have proposed fractional PIλDμ controllers based on fractional calculus to replace classical PI and PID controllers. The closed-loop control of different benchmark dynamic systems using optimally-tuned fraction

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9

Sikaneta, Ishuwa Christopher. "From fractional calculus to split dimensional regularization." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape15/PQDD_0012/MQ31867.pdf.

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10

Beig, Mirza Tanweer Ahmad. "Fractional Calculus and Dynamic Approach to Complexity." Thesis, University of North Texas, 2015. https://digital.library.unt.edu/ark:/67531/metadc822832/.

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Fractional calculus enables the possibility of using real number powers or complex number powers of the differentiation operator. The fundamental connection between fractional calculus and subordination processes is explored and affords a physical interpretation for a fractional trajectory, that being an average over an ensemble of stochastic trajectories. With an ensemble average perspective, the explanation of the behavior of fractional chaotic systems changes dramatically. Before now what has been interpreted as intrinsic friction is actually a form of non-Markovian dissipation that automat

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11

Dreisigmeyer, David W. "Volterra series fractional mechanics." Access citation, abstract and download form; downloadable file 1.54 Mb, 2004. http://wwwlib.umi.com/dissertations/fullcit/3131668.

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12

Hartter, Beverly Jo Dossey John A. "Concept image and concept definition for the topic of the derivative." Normal, Ill. Illinois State University, 1995. http://wwwlib.umi.com/cr/ilstu/fullcit?p9603516.

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Thesis (Ph. D.)--Illinois State University, 1995.<br>Title from title page screen, viewed May 2, 2006. Dissertation Committee: John A. Dossey (chair), Stephen H. Friedberg, Beverly S. Rich, Kenneth Strand, Jane O. Swafford. Includes bibliographical references (leaves 93-97) and abstract. Also available in print.

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13

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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14

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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15

Borthwick, Martin Francis. "Application of fractional calculus to rainfall-streamflow modelling." Thesis, University of Plymouth, 2010. http://hdl.handle.net/10026.1/1823.

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There is evidence that hydrologic systems exhibit memory processes that may be represented by fractional order systems. A new theory is developed in this work that generalises the classical unit hydrograph technique for the rainfall-runoff transformation. The theory is based upon a fractional order linear deterministic systems approach subject to an initial condition and is taken to apply to the entire rainfallstreamflow transformation (i.e. including baseflow). The general equation for a cascade of time-lagged linear reservoirs of fractional order subject to a constant initialisation function

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16

Moshrefi-Torbati, Mohamed. "Fractional calculus and its applications to dynamic systems." Thesis, University of Southampton, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.296421.

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17

Sengul, Sevgi. "Discrete Fractional Calculus and Its Applications to Tumor Growth." TopSCHOLAR®, 2010. http://digitalcommons.wku.edu/theses/161.

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Almost every theory of mathematics has its discrete counterpart that makes it conceptually easier to understand and practically easier to use in the modeling process of real world problems. For instance, one can take the "difference" of any function, from 1st order up to the n-th order with discrete calculus. However, it is also possible to extend this theory by means of discrete fractional calculus and make n- any real number such that the ½-th order difference is well defined. This thesis is comprised of five chapters that demonstrate some basic definitions and properties of discrete fractio

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18

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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19

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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20

Bastos, Nuno Rafael de Oliveira. "Fractional calculus on time scales - Cálculo fraccional em escalas temporais." Doctoral thesis, Universidade de Aveiro, 2012. http://hdl.handle.net/10773/8566.

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Doutoramento em Matemática<br>Introduzimos um cálculo das variações fraccional nas escalas temporais ℤ e (hℤ)!. Estabelecemos a primeira e a segunda condição necessária de optimalidade. São dados alguns exemplos numéricos que ilustram o uso quer da nova condição de Euler–Lagrange quer da nova condição do tipo de Legendre. Introduzimos também novas definições de derivada fraccional e de integral fraccional numa escala temporal com recurso à transformada inversa generalizada de Laplace.<br>We introduce a discrete-time fractional calculus of variations on the time scales ℤ and (ℎℤ)!. First a

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21

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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22

Meoli, Alessandra. "On fractional probabilistic mean value theorems, fractional counting processes and related results." Doctoral thesis, Universita degli studi di Salerno, 2017. http://hdl.handle.net/10556/2621.

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2015 - 2016<br>The thesis collects the outcomes of the author’s research carried out in the research group Probability Theory and Mathematical Statistics at the Department of Mathematics, University of Salerno, during the doctoral programme “Mathematics, Physics and Applications”. The results are at the interface between Fractional Calculus and Probability Theory. While research in probability and applied ﬁelds is now well established and enthusiastically supported, the subject of fractional calculus, i.e. the study of an extension of derivatives and integrals to any arbitrary real or complex

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23

Bologna, Mauro. "The Dynamic Foundation of Fractal Operators." Thesis, University of North Texas, 2003. https://digital.library.unt.edu/ark:/67531/metadc4235/.

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The fractal operators discussed in this dissertation are introduced in the form originally proposed in an earlier book of the candidate, which proves to be very convenient for physicists, due to its heuristic and intuitive nature. This dissertation proves that these fractal operators are the most convenient tools to address a number of problems in condensed matter, in accordance with the point of view of many other authors, and with the earlier book of the candidate. The microscopic foundation of the fractal calculus on the basis of either classical or quantum mechanics is still unknown, and

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24

Pooseh, Shakoor. "Computational methods in the fractional calculus of variations and optimal control." Doctoral thesis, Universidade de Aveiro, 2013. http://hdl.handle.net/10773/11510.

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Doutoramento em Matemática<br>The fractional calculus of variations and fractional optimal control are generalizations of the corresponding classical theories, that allow problem modeling and formulations with arbitrary order derivatives and integrals. Because of the lack of analytic methods to solve such fractional problems, numerical techniques are developed. Here, we mainly investigate the approximation of fractional operators by means of series of integer-order derivatives and generalized finite differences. We give upper bounds for the error of proposed approximations and study their effi

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25

Adams, Jay L. "Hankel Operators for Fractional-Order Systems." University of Akron / OhioLINK, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=akron1248198109.

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26

Wu, Fang. "NABLA Fractional Calculus and Its Application in Analyzing Tumor Growth of Cancer." TopSCHOLAR®, 2012. http://digitalcommons.wku.edu/theses/1217.

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This thesis consists of six chapters. In the first chapter, we review some basic definitions and concepts of fractional calculus. Then we introduce fractional difference equations involving the Riemann-Liouville operator of real number order between zero and one. In the second chapter, we apply the Brouwer fixed point and Contraction Mapping Theorems to prove that there exists a solution for up to the first order nabla fractional difference equation with an initial condition. In chapter three, we define a lower and an upper solution for up to the first order nabla fractional difference equatio

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27

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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28

Uyanik, Meltem. "Analysis of Discrete Fractional Operators and Discrete Fractional Rheological Models." TopSCHOLAR®, 2015. http://digitalcommons.wku.edu/theses/1491.

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This thesis is comprised of two main parts: Monotonicity results on discrete fractional operators and discrete fractional rheological constitutive equations. In the first part of the thesis, we introduce and prove new monotonicity concepts in discrete fractional calculus. In the remainder, we carry previous results about fractional rheological models to the discrete fractional case. The discrete method is expected to provide a better understanding of the concept than the continuous case as this has been the case in the past. In the first chapter, we give brief information about the main result

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29

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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Lebovits, Joachim. "Stochastic calculus with respect to multi-fractional Brownian motion and applications to finance." Phd thesis, Châtenay-Malabry, Ecole centrale de Paris, 2012. http://tel.archives-ouvertes.fr/tel-00704526.

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The aim of this PhD Thesis was to build and develop a stochastic calculus (in particular a stochastic integral) with respect to multifractional Brownian motion (mBm). Since the choice of the theory and the tools to use was not fixed a priori, we chose the White Noise theory which generalizes, in the case of fractional Brownian motion (fBm) , the Malliavin calculus. The first chapter of this thesis presents several notions we will use in the sequel.In the second chapter we present a construction as well as the main properties of stochastic integral with respect to harmonizable mBm.We also give

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31

Nissilä, J. (Juhani). "Fractional calculus and generalised norms in condition monitoring of a load haul dumper." Master's thesis, University of Oulu, 2015. http://urn.fi/URN:NBN:fi:oulu-201504021282.

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This thesis combines the concepts of fractional calculus, norms and means of vectors and machine condition monitoring. Fractional calculus is a branch of calculus that studies the concept of generalising differentiation and integration to arbitrary order. It is as old a discipline as classical calculus although not as widely known. Norm is a generalisation of the length or size of a mathematical object and it provides a single positive value to measure it. Machine condition monitoring is a discipline which focuses on extracting information mainly from industrial machines with noninvasive metho

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32

Arslan, Aykut. "Discrete Fractional Hermite-Hadamard Inequality." TopSCHOLAR®, 2017. http://digitalcommons.wku.edu/theses/1940.

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This thesis is comprised of three main parts: The Hermite-Hadamard inequality on discrete time scales, the fractional Hermite-Hadamard inequality, and Karush-Kuhn- Tucker conditions on higher dimensional discrete domains. In the first part of the thesis, Chapters 2 & 3, we define a convex function on a special time scale T where all the time points are not uniformly distributed on a time line. With the use of the substitution rules of integration we prove the Hermite-Hadamard inequality for convex functions defined on T. In the fourth chapter, we introduce fractional order Hermite-Hadamard ine

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33

Morlanes, José Igor. "Some Extensions of Fractional Ornstein-Uhlenbeck Model : Arbitrage and Other Applications." Doctoral thesis, Stockholms universitet, Statistiska institutionen, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-147437.

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This doctoral thesis endeavors to extend probability and statistical models using stochastic differential equations. The described models capture essential features from data that are not explained by classical diffusion models driven by Brownian motion. New results obtained by the author are presented in five articles. These are divided into two parts. The first part involves three articles on statistical inference and simulation of a family of processes related to fractional Brownian motion and Ornstein-Uhlenbeck process, the so-called fractional Ornstein-Uhlenbeck process of the second kind

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Consiglio, Armando. "Time-fractional diffusion equation and its applications in physics." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/13704/.

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In physics, process involving the phenomena of diffusion and wave propagation have great relevance; these physical process are governed, from a mathematical point of view, by differential equations of order 1 and 2 in time. By introducing a fractional derivatives of order $\alpha$ in time, with $0 < \alpha < 1$ or $1 <= \alpha <= 2$, we lead to process in mathematical physics which we may refer to as fractional phenomena; this is not merely a phenomenological procedure providing an additional fit parameter. The aim of this thesis is to provide a description of such phenomena adopting a mathe

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35

Khan, Mumtaz Ahmad, and Bhagwat Swaroop Sharma. "A study of three variable analogues of certain fractional integral operators." Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/95821.

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The paper deals with a three variable analogues of certain fractional integral operators introduced by M. Saigo. Resides giving three variable analogues of earlier known fractional integral operators of one variable as a special cases of newly defined operators, the paper establishes certain results in the form of theorems including integration by parts.

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36

Amsheri, Somia Muftah Ahmed. "Fractional calculus operator and its applications to certain classes of analytic functions : a study on fractional derivative operator in analytic and multivalent functions." Thesis, University of Bradford, 2013. http://hdl.handle.net/10454/6320.

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The main object of this thesis is to obtain numerous applications of fractional derivative operator concerning analytic and ρ-valent (or multivalent) functions in the open unit disk by introducing new classes and deriving new properties. Our finding will provide interesting new results and indicate extensions of a number of known results. In this thesis we investigate a wide class of problems. First, by making use of certain fractional derivative operator, we define various new classes of ρ-valent functions with negative coefficients in the open unit disk such as classes of ρ-valent starlike f

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Amsheri, Somia M. A. "Fractional calculus operator and its applications to certain classes of analytic functions. A study on fractional derivative operator in analytic and multivalent functions." Thesis, University of Bradford, 2013. http://hdl.handle.net/10454/6320.

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The main object of this thesis is to obtain numerous applications of fractional derivative operator concerning analytic and -valent (or multivalent) functions in the open unit disk by introducing new classes and deriving new properties. Our finding will provide interesting new results and indicate extensions of a number of known results. In this thesis we investigate a wide class of problems. First, by making use of certain fractional derivative operator, we define various new classes of -valent functions with negative coefficients in the open unit disk such as classes of -valent starlike func

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Papakokkinou, Maria. "Portfolio theory subject to value at risk constraints and some financial applications of fractional calculus." Thesis, Imperial College London, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.419782.

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Yu, Qiang. "Numerical simulation of anomalous diffusion with application to medical imaging." Thesis, Queensland University of Technology, 2013. https://eprints.qut.edu.au/62068/1/Qiang_Yu_Thesis.pdf.

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The first objective of this project is to develop new efficient numerical methods and supporting error and convergence analysis for solving fractional partial differential equations to study anomalous diffusion in biological tissue such as the human brain. The second objective is to develop a new efficient fractional differential-based approach for texture enhancement in image processing. The results of the thesis highlight that the fractional order analysis captured important features of nuclear magnetic resonance (NMR) relaxation and can be used to improve the quality of medical imaging.

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Hu, Ke. "On an equation being a fractional differential equation with respect to time and a pseudo-differential equation with respect to space related to Lévy-type processes." Thesis, Swansea University, 2012. https://cronfa.swan.ac.uk/Record/cronfa43021.

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Mukhopadhyay, Shayok. "Fractional Order Modeling and Control: Development of Analog Strategies for Plasma Position Control of the Stor-1M Tokamak." DigitalCommons@USU, 2009. https://digitalcommons.usu.edu/etd/460.

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This work revolves around the use of fractional order calculus in control science. Techniques such as fractional order universal adaptive stabilization (FO-UAS), and the fascinating results of their application to real-world systems, are presented initially. A major portion of this work deals with fractional order modeling and control of real-life systems like heat flow, fan and plate, and coupled tank systems. The fractional order models and controllers are not only simulated, they are also emulated using analog hardware. The main aim of all the above experimentation is to develop a fractiona

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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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Acar, Nihan. "Development of Nabla Fractional Calculus and a New Approach to Data Fitting in Time Dependent Cancer Therapeutic Study." TopSCHOLAR®, 2012. http://digitalcommons.wku.edu/theses/1146.

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The aim of this thesis is to develop discrete fractional models of tumor growth for a given data and to estimate parameters of these models in order to have better data tting. We use discrete nabla fractional calculus because we believe the discrete counterpart of this mathematical theory will give us a better and more accurate outcome. This thesis consists of ve chapters. In the rst chapter, we give the history of the fractional calculus, and we present some basic de nitions and properties that are used in this theory. We de ne nabla fractional exponential and then nabla fractional trigonomet

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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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Camargo, Rubens de Figueiredo. "Calculo fracionario e aplicações." [s.n.], 2009. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307012.

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Orientadores: Edmundo Capelas de Oliveira, Ary Orozimbo Chiacchio<br>Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica<br>Made available in DSpace on 2018-08-12T21:42:46Z (GMT). No. of bitstreams: 1 Camargo_RubensdeFigueiredo_D.pdf: 9956358 bytes, checksum: 45d7b7d76ae44d9b713d341ffc7a1ad5 (MD5) Previous issue date: 2009<br>Resumo: Apresentamos neste trabalho um estudo sistemático e detalhado sobre integrais e derivadas de ordens arbitrárias, o assim chamado cálculo de ordem não-inteira, popularizado com o nome de Cálculo Fraci

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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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BOLOGNA, Emanuela. "Multiscale Biomechanical Characterization of Ligaments and Tendons of the Human Knee." Doctoral thesis, Università degli Studi di Palermo, 2020. http://hdl.handle.net/10447/437545.

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Zemčíková, Michaela. "Kvalitativní a numerická analýza zlomkových diferenciálních rovnic." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2013. http://www.nusl.cz/ntk/nusl-230944.

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This master's thesis deals with fractional differential equations. One of the aims of this thesis is to mention summary of basic types of fractional differential equations. It is very difficult to find their exact solution, hence we will analyze the main qualitative properties of solution, which are stability and asymptotics. Part of the text will be devoted to fractional difference equations, i.e. discussion of numerical solution. At the end of thesis the Bagley-Torvik model will be described with respect to qualitative properties and numerical solution.

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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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Kuroda, Lucas Kenjy Bazaglia. "Nova modelagem fracionária aplicada à dinâmica tumoral (HPV 16)." Botucatu, 2020. http://hdl.handle.net/11449/192191.

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Orientador: Rubens de Figueiredo Camargo<br>Resumo: O presente trabalho apresenta a nova modelagem fracionária, que considera propriedades hereditárias e efeitos de memória, no modelo de Gompertz, para descrever a evolução do câncer causado pela infecção do HPV 16. Devido a variabilidade do desenvolvimento do câncer em humanos, utiliza-se o crescimento in vivo do tumor em camundongo transgênico que expressam os oncogenes E6 e E7 tratados com DMBA / TPA (inicializador e promotor do HPV 16) para capturar as características gerais dessa variabilidade. Resultados mostram que a inserção de um novo

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