The Well-Posedness of Fractional Systems with Affine-Periodic Boundary Conditions

Affine-Periodic Boundary Value Problem for a Fractional Differential Inclusion

“…The affine period is widely used in astrophysics. For some interesting results on the affine period, please refer to [12][13][14][15] and the references therein. In [12], using the lower and upper solutions method and topological degree theory, Xu et al claimed that a Newton affine-periodic system admits an affine-periodic; In [13], Liu et al showed that every first-order dissipative-(T, a)affine-periodic system also has a dissipative-(T, a)-affine-periodic solution in [0, ∞) using topological degree theory and the lower and upper solutions method; In [14], Xu et al firstly gave some extremum principles for higher-order affine-periodic systems.…”

“…Then, using these extremum principles, the authors studied the existence of affine-periodic solutions for n(n ∈ N)-order ordinary differential equations. A class of nonlinear fractional dynamical systems with affine-periodic boundary conditions were considered by Xu et al in [15]. Using the homotopy invariance of the Brouwer degree, the authors gained the existence of solutions to the fractional dynamical systems, while using Gronwall-Bellman inequality, the uniqueness of the solution was also obtained.…”