Generalized Antiperiodic Boundary Value Problems for the Fractional Differential Equation with p-Laplacian Operator

Fractional differential equations arise in various areas of science and engineering, such as physics, mechanics, chemistry, and engineering. The fractional order models become more realistic and practical than the classical integer models. Due to their applications, fractional differential equations have gained considerable attentions; one can see [1–14] and references therein. Anti-periodic boundary value problems occur in the mathematical modeling of a variety of physical processes. Anti-periodic problems constitute an important class of boundary value problems and have received considerable attention (see [15–19]). In [20], Zhang considered the existence and multiplicity results of positive solutions for the following boundary value problem of fractional differential equation: