On existence of positive solution for initial value problem of nonlinear fractional differential equations of order \(1 < \alpha \leq 2\). (English) Zbl 1340.34031

Matar, M. M.

Acta Math. Univ. Comen., New Ser. 84, No. 1, 51-57 (2015).

The existence and uniqueness of positive solutions are studied for nonlinear fractional differential equations on finite intervals. The method of upper and lower solutions, and Schauder and Banach fixed point theorems are used. An illustrative example is presented as well.

Reviewer: Michal Fečkan (Bratislava)

MSC:

34A08	Fractional ordinary differential equations
34A12	Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
47N20	Applications of operator theory to differential and integral equations

Keywords:

fractional differential equations; positive solution; upper and lower solutions; existence and uniqueness