Faculté des Mathématiques et de l'Informatiquehttp://dspace.univ-msila.dz:8080//xmlui/handle/123456789/152019-06-19T00:47:02Z2019-06-19T00:47:02ZCompatibility of ternary relations with binary fuzzy relationsOmar, Barkathttp://dspace.univ-msila.dz:8080//xmlui/handle/123456789/143922019-06-18T14:40:58Z2019-05-04T00:00:00ZCompatibility of ternary relations with binary fuzzy relations
Omar, Barkat
Previously, ternary relations did not get enough attention from studies like binary relations, but recently there has been a noticeable turnout. Inspired by the importance of them, our thinking has led to the addition of a contribution to this framework. It means that the main aim of this work is to contribute to the addition of a new study in the field of ternary relations. More specifically, we aim to study the compatibility of a ternary relation with a binary fuzzy relation, similarly to the binary case.
The study of above compatibility requires us to study effective tools to achieve this. In the present thesis, we focused on two of them. We aim to extend the interesting notions of traces and clone relations of a binary relation to the setting of ternary relations. The first study, allow us to characterize the compatibility in terms of traces, where we proved that this compatibility can be expressed in terms of inclusions of the binary fuzzy relation in the traces of the ternary relation . The second one, allow us to represent all the binary fuzzy tolerance relations that a crisp ternary relation is compatible with.
2019-05-04T00:00:00ZInitial value problem for nonlinear implicit fractional differential equations with Katugampola derivativeBasti, Bilalhttp://dspace.univ-msila.dz:8080//xmlui/handle/123456789/140582019-05-28T09:18:35Z2019-01-01T00:00:00ZInitial value problem for nonlinear implicit fractional differential equations with Katugampola derivative
Basti, Bilal
This work studies the existence and uniqueness of solutions for a class of
nonlinear implicit fractional differential equations via the Katugampola fractional
derivatives with an initial condition. The arguments for the study are based upon
the Banach contraction principle, Schauders fi xed point theorem and the nonlinear
alternative of Leray-Schauder type.
2019-01-01T00:00:00ZExistence et unicité de solutions auto-similaires générales pour certaines équations fractionnaires non-linéairesBasti, Bilalhttp://dspace.univ-msila.dz:8080//xmlui/handle/123456789/140572019-05-28T09:14:41Z2019-05-04T00:00:00ZExistence et unicité de solutions auto-similaires générales pour certaines équations fractionnaires non-linéaires
Basti, Bilal
In this thesis, we discuss several existence and uniqueness results of generalized self-similar solutions for some nonlinear partial differential equations of fractional order of Katugampola type, with boundary value, initial value, or with integral conditions in Banach space, we use the Banach contraction principle, Schauder and Guo-Krasnosel'skii fixed point theorems, and the technique of the nonlinear alternative of Leray-Schauder type.
2019-05-04T00:00:00ZOn the Noetherian Properties of Reduction System of WordsGhadbane, Nacerhttp://dspace.univ-msila.dz:8080//xmlui/handle/123456789/139582019-05-14T08:10:25Z2018-12-01T00:00:00ZOn the Noetherian Properties of Reduction System of Words
Ghadbane, Nacer
For any set of symbols, denotes the set of all words of symbols over , including
the empty string . The set denotes the free monoid generated by under the operation of
concatenation with the empty string serving as identity.
Let R be a nite set. We de ne the binary relation )R
as follows, where u; v 2 : u)R
v
if there exist x; y 2 and (l;m) 2 R with u = xly and v = xmy. The structure
;)R
is a
reduction system of words and the relation )R
is the reduction relation. Let
;)R
be a reduction
system of words. The relation )R
is Noetherian if there is no in nite sequence w0;w1; ::: 2 such
that for all i 0;wi)R
wi+1.
In this paper, we study properties of reduction systems of words and give conditions under which
a reduction system of word is Noetherian.
2018-12-01T00:00:00Z