Complex variable approach to the analysis of a fractional differential equation in the real line

Müfit Şan

doi:10.1016/j.crma.2018.01.008

Complex analysis/Functional analysis

Complex variable approach to the analysis of a fractional differential equation in the real line
[Approche par variable complexe de l'analyse d'une équation différentielle fractionnaire sur la droite réelle]

Présenté par : the Editorial Board

Müfit Şan ¹

¹ Department of Mathematics, Faculty of Science, Çankırı Karatekin University, TR-18100, Çankırı, Turkey

Comptes Rendus. Mathématique, Volume 356 (2018) no. 3, pp. 293-300.

Résumé
Abstract

L'objectif principal de ce travail est d'établir un théorème d'existence de type Peano pour un problème aux valeurs initiales faisant intervenir une dérivée fractionnaire, puis, comme conséquence, de donner une réponse partielle à l'existence locale d'une solution continue du problème aux valeurs initiales suivant :

{\begin{matrix} D_{x}^{q} u (x) = f (x, u (x)), \\ u (0) = b, (b \neq 0) . \end{matrix}

De plus, nous étudions les propriétés géométriques des solutions pour quelques cas particuliers.

The first aim of this work is to establish a Peano-type existence theorem for an initial value problem involving a complex fractional derivative, and then, as a consequence of this theorem, to give a partial answer for the local existence of the continuous solution to the initial value problem:

{\begin{matrix} D_{x}^{q} u (x) = f (x, u (x)), \\ u (0) = b, (b \neq 0) . \end{matrix}

Moreover, for some special cases of the problem, we investigate the corresponding geometric properties of the solutions.

Reçu le : 2016-05-18
Accepté le : 2018-01-19
Publié le : 2018-02-01

DOI : 10.1016/j.crma.2018.01.008

Affiliations des auteurs :

Müfit Şan ¹

¹ Department of Mathematics, Faculty of Science, Çankırı Karatekin University, TR-18100, Çankırı, Turkey

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     title = {Complex variable approach to the analysis of a fractional differential equation in the real line},
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     pages = {293--300},
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Müfit Şan. Complex variable approach to the analysis of a fractional differential equation in the real line. Comptes Rendus. Mathématique, Volume 356 (2018) no. 3, pp. 293-300. doi : 10.1016/j.crma.2018.01.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2018.01.008/

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