Generalized antiperiodic boundary value problems for the fractional differential equation with \(p\)-Laplacian operator
Summary: We discuss the existence of solutions about generalized antiperiodic boundary value problems for the fractional differential equation with \(p\)-Laplacian operator \(\phi_p(^cD^\alpha_{0+}u(t)) = f(t, u(t), u'(t)), 0 < t < T, 1 < \alpha \leq 2, u(0) + (-1)^\theta au(T) = 0, ^cD^\beta_{0+} u(0) + (-1)^\theta b ^cD^\beta_{0+} u(T) = \lambda, 0 < \beta < 1\), where \(^cD^\alpha_{0+}\) is the Caputo fractional derivative, \(\theta = 0, 1, a > 0, a \neq 1, b > 0\) and \(\phi_p(s) = |s|^{p-2}s, p > 1, \phi^{-1}_p = \phi_q, 1/p + 1/q = 1\). Our results are based on fixed point theorem and contraction mapping principle. Furthermore, three examples are also given to illustrate the results.
scientific article; zbMATH DE number 6175065