In this paper, we introduce a new concept of nonlocal anti-periodic boundary
conditions and solve fractional and sequential fractional differential
equations supplemented with these conditions. The anti-periodic boundary
conditions involve a nonlocal intermediate point together with one of the
fixed end points of the interval under consideration, and accounts for a
flexible situation concerning anti-periodic phenomena. The existence results
for the given problems are obtained with the aid of standard fixed point
theorems. Some examples illustrating the main results are also discussed.
The paper concludes with several interesting observations.
Existence of solutions for nonlinear fractional differential equations with impulses and anti-periodic boundary conditions
