Several results for high dimensional singular fractional systems involving $n^2$ Caputo derivatives

Amele TAÏEB

doi:10.26637/MJM0603/0017

Several results for high dimensional singular fractional systems involving $n^2$ Caputo derivatives

Authors :

Amele TAÏEB

Author Address :

LPAM, Faculty ST, UMAB Mostaganem, Algeria.

Abstract :

In this paper, we introduce a high dimensional systems of singular fractional nonlinear differential equations involving $n^2$ Caputo derivatives. Using Schauder fixed point theorem and the contraction mapping principle, we investigate new existence and uniqueness results. Furthermore, we define and study the Ulam-Hyers stability and the generalized Ulam-Hyers stability for such systems. The application of the main results is illustrated by some examples.

Keywords :

Caputo derivative, fixed point, singular fractional differential equation, existence, uniqueness, Ulam-Hyers stability, generalized Ulam-Hyers stability.

DOI :

10.26637/MJM0603/0017

Article Info :

Received : January 09, 2018; Accepted : June 22, 2018.