TY  - JOUR
ID  - Denton2016
LB  - Denton2016
AU  - Denton, Zachary
TI  - Monotone method for Riemann-Liouville multi-order fractional differential systems
ST  - Monotone method for Riemann-Liouville multi-order fractional differential systems
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2016
VL  - 36
IS  - 2
SP  - 189
EP  - 206
DO  - http://dx.doi.org/10.7494/OpMath.2016.36.2.189
UR  - http://dx.doi.org/10.7494/OpMath.2016.36.2.189
AB  - In this paper we develop the monotone method for nonlinear multi-order \(N\)-systems of Riemann-Liouville fractional differential equations. That is, a hybrid system of nonlinear equations of orders \(q_i\) where \(0 \lt q_i \lt 1\). In the development of this method we recall any needed existence results along with any necessary changes. Through the method's development we construct a generalized multi-order Mittag-Leffler function that fulfills exponential-like properties for multi-order systems. Further we prove a comparison result paramount for the discussion of fractional multi-order inequalities that utilizes lower and upper solutions of the system. The monotone method is then developed via the construction of sequences of linear systems based on the upper and lower solutions, and are used to approximate the solution of the original nonlinear multi-order system.
KW  - fractional differential systems
KW  - multi-order systems
KW  - lower and upper solutions
KW  - monotone method
SN  - 1232-9274
ER  -