Existence of multiple weak solutions for a class of fractional boundary value problems with Laplace operator

Abstract This paper investigates the existence of multiple weak solutions for a class of fractional boundary value problems that not only involve fractional derivatives with respect to time but also include the Laplace operator in spatial variables. By employing variational methods and critical point theory, this study constructs a derivative space that includes both time and spatial variables, which is different from previous constructions that focused only on time. The results demonstrate the existence of at least three weak solutions, or even infinitely many weak solutions, under certain assumptions on the nonhomogeneous term.