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Resolution des equations d’etat lineaires d’ordre fractionnaire

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dc.contributor.author Boucherma, Djamel
dc.contributor.author Charef, Abdelfatah
dc.date.accessioned 2022-05-24T09:50:02Z
dc.date.available 2022-05-24T09:50:02Z
dc.date.issued 2017-06-29
dc.identifier.uri http://depot.umc.edu.dz/handle/123456789/5724
dc.description.abstract In this work, the resolution of the fractional state space equation representing the linear fractional systems of commensurate order, for all the eigenvalues types of the state matrix A and the order of differentiation m was proposed. The explicit expressions of the homogeneous and non-homogeneous solutions of this fractional state space equation were developed. For different values of the state-space matrix A eigenvalues and the order m, the obtained solutions are linear combinations of suitable fractional fundamental functions whose Laplace transforms are irrational functions. The approximations of these irrational functions by rational functions were obtained so that the solutions of the fractional state space equation are linear combinations of classical exponential, cosine, sine, damped cosine and damped sine functions. Illustrative examples for all the eigenvalues types of the state matrix A and the order m were presented and the results obtained were very satisfactory.
dc.language.iso fr
dc.publisher Université Frères Mentouri - Constantine 1
dc.subject الأنظمة الخطية ذات الأس الجزئي المتعادل
dc.subject التحلل الشكلي
dc.subject تمثيل حل لمعادلة فضاء الحالة ذات الأس الجزئي، دالة غير كسرية
dc.subject دالة كسرية
dc.subject القيم الذاتية
dc.subject نظرية Hamilton Cayley
dc.subject Cayley-Hamilton theorem
dc.subject Eigenvalues
dc.subject Fractional state space equation of commensurate order representation
dc.subject Fractional system of commensurate order;
dc.subject Irrational function
dc.subject Modal decomposition
dc.subject Rational function
dc.subject Rational function
dc.subject Décomposition modale
dc.subject Fonction irrationnelle
dc.subject Représentation d’état fractionnaire d’ordre commensurable
dc.subject Système fractionnaire d’ordre commensurable
dc.subject Théorème de Cayley-Hamilton
dc.subject Valeurs propres
dc.title Resolution des equations d’etat lineaires d’ordre fractionnaire
dc.type Thesis

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