Multiplicity of solutions for fractional-order differential equations via the k(x)-Laplacian operator and the genus theory

Date

2022

Authors

Srivastava, H.M.
da Costa Sousa, Jose Vanterler

Journal Title

Journal ISSN

Volume Title

Publisher

Fractal and Fractional

Abstract

In this paper, we investigate the existence and multiplicity of solutions for a class of quasi-linear problems involving fractional differential equations in the x-fractional space (H y,β;x k(x)) (△). Using the Genus Theory, the Concentration-Compactness Principle, and the Mountain Pass Theorem, we show that under certain suitable assumptions the considered problem has at least k pairs of non-trivial solutions.

Description

Keywords

fractional differential equations, k(x)-Laplacian, x-Hilfer fractional derivative, existence, multiplicity of solutions, genus theory, Concentration-Compactness Principle, Mountain Pass Theorem, variable exponents, variational methods

Citation

Srivastava, H. & da Costa Sousa, J. (2022). “Multiplicity of solutions for fractionalorder differential equations via the k(x)-Laplacian operator and the genus theory.” Fractal and Fractional, 6(9), 481. https://doi.org/10.3390/fractalfract6090481