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

Abdelali Sabri

LM2CE, Department of Economics, Faculty of Economics and Management, Hassan first University, B.P. 764, Settat, Morocco

Email address: abdelali.sabri21@gmail.com

Doi : https://doi.org/10.47013/16.3.5

Cited by : Jordan J. Math & Stat., 16 (3) (2023), 445 - 462

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Received on: June 23, 2022;                                         Accepted on: Sept. 19, 2022

 Abstract. The aim of this paper is to 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.

Keywords: Existence, fractional p(x)-Laplacian, fractional Sobolev space, uniqueness, variable exponent, variable order, weak solution.