TY - JOUR
T1 - Discontinuous Fractional Sturm-Liouville Problems with Hilfer Derivatives
AU - Zhou , Le
AU - Hao , Xiaoling
AU - Li , Kun
JO - Journal of Nonlinear Modeling and Analysis
VL - 3
SP - 775
EP - 792
PY - 2024
DA - 2024/08
SN - 6
DO - http://doi.org/10.12150/jnma.2024.775
UR - https://global-sci.org/intro/article_detail/jnma/23362.html
KW - Sturm-Liouville problem, Hilfer derivatives, eigenparameter, fractional boundary conditions, fractional transmission conditions.
AB - <p style="text-align: justify;">In this paper, we study discontinuous Sturm-Liouville problem
with fractional Hilfer derivatives. By defining an operator $A$ in the Hilbert
space $L_2[−1, 1],$ this research shows that the eigenvalues and corresponding
eigenfunctions of the main problem coincide with the eigenvalues and corresponding eigenfunctions of the constructed operator. Moreover, the characteristic function is also constructed such that the eigenvalues of the problem
are coincide with the zeros of this function.</p>