Boundary value problem with fractional p-Laplacian operator

Abstract

The aim of this paper is to obtain the existence of solution for the fractional p-Laplacian Dirichlet problem with mixed derivatives tDTα(|0Dtαu(t)|p-20Dtαu(t)) = f(t,u(t)), t ∈ [0,T], u(0) = u(T) = 0, where 1/p < α < 1, 1 < p < ∞ and f : [0,T] × ℝ → ℝ is a Carathéodory function which satisfies some growth conditions. We obtain the existence of nontrivial solutions by using the direct method in variational methods and mountain pass theorem.

Keywords

• fractional calculus
• mixed fractional derivatives
• boundary value problem
• p-laplacian operator
• mountain pass theorem
• 26a33
• 58e05
• 65l10