On a nonlinear fractional differential equation on partially ordered metric spaces

By Dumitru Băleanu, H. Mohammadi, Sh. Rezapour. Advances in Differential Equations, 2013

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In this paper, by using a fixed point result on ordered metric spaces, we prove the existence and uniqueness of a solution of the nonlinear fractional differential equation Dαu(t)=f(t,u(t)) (t∈I=[0,T], 0<α<1) via the periodic boundary condition u(0)=0, where T>0 and f:I×R→R is a continuous increasing function and Dαc denotes the Caputo fractional derivative of order α. Also, we solve it by using the anti-periodic boundary conditions u(0)+u(T)=0 with u(0)≤0 and u(0)+μu(T)=0 with u(0)≤0 and μ>0 separately.

Subfields: Applied Mathematics, Geometry and Topology, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/c6e1d6d994ec23c889ec37202febb1ea7736cbb5