On a Class of Degenerate Fractional p(.)-Laplacian Problems with Variable order and Variable Exponent

Abstract

Theaimofthis paper isto study a class of a degenerate elliptic problem driven by the fractional p(.)-Laplacian operator with variable order and variable exponent, the main tool used here is the variational method combined with the theory of variable-order fractional Sobolev spaces with variable exponent.

Key words and phrases. Existence, fractional p(x)-Laplacian, fractional Sobolev space, uniqueness, variable exponent, variable order, weak solution.

2010 Mathematics Subject Classification. 34A08, 35A15, 46E35, 35R11, 35S15