| Titre : | Fractional Stochastic Differential Equations |
| Auteurs : | S. Idrissi, Directeur de thèse ; Souiah, Salah Eddine, Auteur |
| Type de document : | texte imprimé |
| Editeur : | université Dr mouley tahar, Faculté des Sciences, Saida, Algerie : Alger: univ-saida, 2019 |
| Format : | 51 p. / 27 Cm. |
| Accompagnement : | + Cd. |
| Note générale : | Appendix; Biblioghraphy |
| Langues: | Anglais |
| Mots-clés: | Mathématique ; Fractional stochastic differential equations ; Existence and uniqueness of solutions ; Temporally weighted norm ; Fractional calculus ; Caputo fractional derivative. |
| Résumé : |
This master thesis focused on the study of the existence and the uniqueness of solution for a class of fractional stochastic differential equation. First, we brought the reader through the fundamental notions of stochastic processes and stochastic integration as well as stochastic differential equations. Then we gave a global view on the fractional calculus, after a short introduction and some preliminaries, we explored the Gr ̈u unwald-Letnikov, Riemann-Liouville and Caputo approaches for defining a fractional derivative. Then, we proved some basic properties of fractional derivatives, such as linearity, the Leibniz rule and composition. Thereafter, we applied the definitions of the fractional derivatives to a few examples. As application of fractional derivatives we gave a commonly used economic model. This master thesis ends with investigating a global result on the existence and uniqueness of solutions for Caputo fractional stochastic differential equations of order α ∈ (1/2, 1) whose coefficients satisfy a standard Lipschitz condition, and using a temporally weighted norm. |
| Note de contenu : |
1 Preliminary Background 2 Fractional Calculus 3 Stochastic Fractional Differential Equations 4 Conclusion |
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