Srivastava, H.M.da Costa Sousa, Jose Vanterler2022-11-132022-11-1320222022Srivastava, 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/fractalfract6090481https://doi.org/10.3390/fractalfract6090481http://hdl.handle.net/1828/14449In 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.enfractional differential equationsk(x)-Laplacianx-Hilfer fractional derivativeexistencemultiplicity of solutionsgenus theoryConcentration-Compactness PrincipleMountain Pass Theoremvariable exponentsvariational methodsArticle