# Solvability For Nonlinear Systems Of Differential Equations With Two Arbitrary Orders

### New Zealand Journal of Mathematics

Vol. 46, (2016), Pages 115-128

Mohamed Amin Abdellaoui

LPAM, Faculty SEI,

UMAB Mostaganem,

Algeria.

Zoubir Dahmani

LPAM, Faculty SEI,

UMAB Mostaganem,

Algeria.

Abstract In this paper we study a coupled system of nonlinear differential equations of two arbitrary orders $\alpha, \beta \in \mathbb{R^+}-\mathbb{N}$. New existence and uniqueness results are established using Banach fixed point theorem. Other existence results are obtained using Schaefer and Krasnoselskii fixed point theorems. Some illustrative examples are also presented.

Keywords Caputo derivative, Banach fixed point theroem, coupled system, existence, uniqueness.

Classification (MSC2000) 34A34, 34B10.