Iterative scheme to a coupled system of highly nonlinear fractional order differential equations. (English) Zbl 1412.34041

Shah, Kamal; Khan, Rahmat

Comput. Methods Differ. Equ. 3, No. 3, 163-176 (2015).

Summary: In this article, we investigate sufficient conditions for the existence of maximal and minimal solutions to a coupled system of highly nonlinear differential equations of fractional order with mixed type boundary conditions. To achieve this goal, we apply monotone iterative technique together with the method of upper and lower solutions. Also an error estimation is given to check the accuracy of the method. We provide an example to illustrate our main results.

MSC:

34A08	Fractional ordinary differential equations
35R11	Fractional partial differential equations

Keywords:

mixed type boundary conditions; upper and lower solutions; monotone iterative technique; existence and uniqueness results