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 evolution equations and analyze the generalized linear evolution equations with non-singular ker- nel derivative. The well-posedness of the extended CFFD linear evolution equation is demonstrated by proving the existence of a solution, the uniqueness of the existing solu- tion, and finally the continuous dependence of the behavior of the solution on the data and parameters. Extended evolution equations with CFFD are applied to kinetics, heat diffusion and dispersion of shallow water waves using MATLAB simulation software for validation purpose. / Mathematical Science / M Sc. (Applied Mathematics)

This work attempts an answer to two questions. Firstly, is it possible to experience meaning when everything is transient? And secondly, in what way is objectivity possible when it comes to such phenomena as existential meaning? The questions originate from our insideperspective, and it is from what we have experienced ourselves that we try to make intelligible existential meaning. We are to a great extent part of the context in which we live. Our ability to contemplate our situation and our own contemplation is taking place in interplay with others. To make room for the small things meaningful in life, the expression existential meaning is used. In this expression both the meaningless and the meaningful are included, since both are needed for our understanding of meaning. Without the Other and that which is different, the individual person’s formation of existential meaning becomes just more of the same, it becomes an enclosure in the present. The encounter with the Other makes room for that which is different to break through. Objectivity is possible when it comes to existential meaning, if one views objectivity as a process between people. It is performed in conversation. Those who converse, refer to their bodily experiences of the Time that remains and help each other, using language as the tool, to formulate their experiences. They compare each others’ manifestations of existential meaning, and with the help of language they go further in the formation of what is meaningless and meaningful. Their conversations imply a normative presupposition that they can justify the claims that they make. Because it is actually not possible to make intelligible existential meaning in words other than by doing it as a mix of descriptions of that which is manifesting itself and linguistic rewritings in the form of stories. This expression of objectivity has a normative aspect, namely in relation to the possibility that we can be wrong. Therefore, we need each other in the act of judging, and together we are guided by the fact that it later on can emerge things that show that our judgment has not been fully correct.

Toni Morrison reinterprets and reconstitutes American history by placing the lives, stories and experiences of African Americans in a position of centrality, while relegating white American history and cultural traditions to the margins of her narratives. She rewrites American history from an alternative - African American woman's - perspective, and subverts the accepted racist and patriarchally inspired `truths' about life, love and women's experiences through her sympathetic depiction of murderous mother love and complex female relationships in Beloved. She writes about oppression, pain and suffering, and of the need for the acknowledgement and alleviation of the various forms of oppression that scar human existence. Morrison's engagement with healing in Beloved forms the central focus of this short dissertation. The novel is analysed in relation to Mary Douglas's `Two Bodies' theory, John Caputo's ideas on progressive Foucaultian hermeneutics and healing gestures, and Julia Martin's thoughts on alternative healing practices based on non-dualism and interconnectedness. Within this interdisciplinary context, Beloved is read as a `small start' to `creative engagement' with alternative healing practices (Martin, 1996:104). / English / M.A. (English)

Notre objectif dans cette thèse est l'étude des équations différentielles non linéaires comportant des dérivées fractionnaires en temps et/ou en espace. Nous nous sommes intéressés dans un premier temps à l'étude de deux systèmes non linéaires d'équations différentielles fractionnaires en temps et/ou en espace, puis à l'étude d'une équation différentielle fractionnaire en temps. Plus exactement pour la première partie, les questions concernant l'existence globale et le comportement asymptotique des solutions d'un système non linéaire d'équations différentielles comportant des dérivées fractionnaires en temps et en espace sont élucidées. Les techniques utilisées reposent sur des estimations obtenues pour les solutions fondamentales et la comparaison de certaines inégalités fractionnaires. Toujours dans la première partie, l'étude d'un système non linéaire d'équations de réaction-diffusion avec des dérivées fractionnaires en espace est abordée. L'existence locale et l'unicité des solutions sont prouvées à l'aide du théorème du point fixe de Banach. Nous montrons que les solutions sont bornées et analysons leur comportement à l'infini. La deuxième partie est consacrée à l'étude d'une équation différentielle fractionnaire non linéaire. Sous certaines conditions sur la donnée initiale, nous montrons que la solution est globale alors que sous d'autres, elle explose en temps fini. Dans ce dernier cas, nous donnons son profil ainsi que des estimations bilatérales du temps d'explosion. Alors que pour la solution globale nous étudions son comportement asymptotique. / Our objective in this thesis is the study of nonlinear differential equations involving fractional derivatives in time and/or in space. First, we are interested in the study of two nonlinear time and/or space fractional systems. Our second interest is devoted to the analysis of a time fractional differential equation. More exactly for the first part, the question concerning the global existence and the asymptotic behavior of a nonlinear system of differential equations involving time and space fractional derivatives is addressed. The used techniques rest on estimates obtained for the fundamental solutions and the comparison of some fractional inequalities. In addition, we study a nonlinear system of reaction-diffusion equations with space fractional derivatives. The local existence and the uniqueness of the solutions are proved using the Banach fixed point theorem. We show that the solutions are bounded and analyze their large time behavior. The second part is dedicated to the study of a nonlinear time fractional differential equation. Under some conditions on the initial data, we show that the solution is global while under others, it blows-up in a finite time. In this case, we give its profile as well as bilateral estimates of the blow-up time. While for the global solution we study its asymptotic behavior.

This paper concentrates on the description of fractional order LTI SISO systems using generalized Laguerre functions. There are properties of generalized Laguerre functions described in the paper, and an orthogonal base of these functions is shown. Next the concept of fractional derivatives is explained. The last part of this paper deals with the representation of fractional order LTI SISO systems using generalized Laguerre functions. Several examples were solved to demonstrate the benefits of using these functions for the representation of LTI SISO systems.

Integrace a derivace jsou obvykle známy pro celočíselný řád (tj. první, druhý, atd.). Existuje ale zobecnění pro zlomkové (neceločíselné) řády, které lze implementovat pomocí elektronických obvodů zlomkového řádu (případně provést jejich aproximaci) a které poskytuje nový stupeň volnosti pro návrh elektronických obvodů. Obvody zlomkového řádu jsou obvykle aproximovány diskrétními součástkami pomocí RC struktur s velkými rozsahy odporů a kapacit, a tím se jeví nepraktické pro použití v integrovaných obvodech. Tato práce prezentuje implementaci obvodů zlomkového řádu v integerovaných obvodech a jejich praktické využití v této oblasti. Jsou použity prvky se soustředěnými parametry (např. RC žebřík) i prvky s rozprostřenými parametery (např. R-PMOScap, skládající se z nesalicidovaného proužku polykrystalického křemíku nad hradlovým oxidem); je použita pouze technologie typu analogvý CMOS bez dodatečných procesních kroků. Užití obvodů zlomkového řádu bylo demonstrováno realizací několika integrovaných napěťových regulátorů, v nichž obvody zlomkového řádu realizují řízení zlomkového řádu za účelem dosažení silné stejnosměrné regulace a dobré stability regulační smyčky - i bez použití kompenzační nuly nebo příliš vysoké externí kapacity (některé napěťové regulátory dovolují i zatěžovací kapacitou v rozsahu nula až nekonečno).

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