Research on solution of boundary value problems of fractional-order differential equations based on fractional-order Laplacian operators

In this paper, a thorough investigation is conducted on the boundary value problem of fractional-order differential equations. The nonlocality and singularity problems related to fractional-order differential operators are overcome, thus expanding the scope of research in the field of fractional-order theory. Furthermore, we examine both the existence and uniqueness aspects concerning solutions for fractional-order differential equations that involve parameters as well as Laplacian operators. Additionally, we explore sufficient conditions necessary to ensure both existence and uniqueness when dealing with equations containing fractional derivatives alongside integral boundary conditions.