Abstract
We discuss the existence and uniqueness of solutions for a fractional differential equation of order
q
∈
(
n
−
1
,
n
]
with slit-strips type boundary conditions. The slit-strips type boundary condition states that the sum of the influences due to finite strips of arbitrary lengths is related to the value of the unknown function at an arbitrary position (nonlocal point) in the slit (a part of the boundary off the two strips). The desired results are obtained by applying standard tools of the fixed point theory and are well illustrated with the aid of examples. We also extend our discussion to the cases of arbitrary number of nonlocal points in the slit, the nonlocal multi-substrips conditions and Riemann-Liouville type slit-strips boundary conditions.
MSC:
34A12, 34A40.