Generalized fractional derivatives and Laplace transform

By Fahd Jarad, Thabet Abdeljawad. Discrete and Continuous Dynamical Systems. Series A, 2020

407 citations recorded by the source corpus.

In 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.

Subfields: Mathematical Physics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/019280e8ffc4834debdea7091a636469e6918ec0

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In Mathematical Physics

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

Weighted Fractional Calculus: A General Class of Operators (2022, methodology): “This terminology is a convenience that will be useful later when we combine these concepts with those of Laplace transforms with respect to functions [42,43] and the corresponding function spaces.”
Existence uniqueness and stability of mild solutions for semilinear ψ-Caputo fractional evolution equations (2020, methodology): “Recently, Jarad and Abdeljawad [39] introduced the generalized Laplace transform with respect to another function and the inverse version of the Laplace transform with respect to another function.”
Nonlinear generalized fractional differential equations with generalized fractional integral conditions (2020, methodology): “We deal in this paper with a recently established ψ-Caputo fractional derivative within the framework of absolutely continuous functions proposed by Jarad and Abdeljawad [21].”