Existence of solutions for nonlinear problems involving mixed fractional derivatives with p(x)-Laplacian operator

Abstract

In this article, a functional boundary value problem involving mixed fractional derivatives with p(x)p\left(x)-Laplacian operator is investigated. Based on the fixed point theorems and Mawhin’s coincidence theory’s extension theory, some existence theorems are obtained in the case of non-resonance and the case of resonance. Some examples are supplied to verify our main results.

Keywords

• functional boundary condition
• p(x)-laplacian
• mixed fractional derivatives
• fixed point theorem
• coincidence degree theory
• 34a05
• 34a12
• 34b15