Jarad, FahdAbdeljawad, Thabet2022-05-112025-09-182022-05-112025-09-182020Jarad, Fahd; Abdeljawad, Thabet (2020). "Generalized fractional derivatives and Laplace transform", Discrete and Continuous Dynamical Systems - Series S, Vol. 13, No. 3, pp. 709-722.1937-16321937-1179https://doi.org/10.3934/dcdss.2020039https://hdl.handle.net/20.500.12416/11564In this article, we study generalized fractional derivatives that contain kernels depending on a function on the space of absolute continuous functions. We generalize the Laplace transform in order to be applicable for the generalized fractional integrals and derivatives and apply this transform to solve some ordinary differential equations in the frame of the fractional derivatives under discussion.eninfo:eu-repo/semantics/openAccessGeneralized Fractional DerivativesGeneralized Caputo Fractional DerivativeGeneralized Laplace TransformArticle10.3934/dcdss.20200392-s2.0-85078898853