Weak solution for nonlinear fractional p(.)-Laplacian problem with variable order via Rothe's time-discretization method

Abstract

In this paper, we prove the existence and uniqueness results of weak solutions to a class of nonlinear fractional parabolic p(.)-Laplacian problem with variable order. The main tool used here is the Rothe’s method combined with the theory of variable-order fractional Sobolev spaces with variable exponent.

Keywords

• fractional p(.)-Laplacian
• fractional Sobolev space
• semi-discretization
• Rothe’s method
• variable exponent
• variable order