Samraiz, MuhammadUmer, MuhammadNaheed, SaimaBaleanu, Dumitru2024-09-182024-09-182023Samraiz, Muhammad...et al (2023). "On Weighted Fractional Operators with Applications to Mathematical Models Arising in Physics", Lecture Notes in Networks and Systems, 5th International Conference On Mathematical Modelling, Applied Analysis And Computation, ICMMAAC 2022, Vol. 666, pp. 53-68.http://hdl.handle.net/20.500.12416/8504In recent study, we develop the weighted generalized Hilfer-Prabhakar fractional derivative operator and explore its key properties. It unifies many existing fractional derivatives like Hilfer-Prabhakar and Riemann-Liouville. The weighted Laplace transform of the newly defined derivative is obtained. By involving the new fractional derivative, we modeled the free-electron laser equation and kinetic equation and then found the solutions of these fractional equations by applying the weighted Laplace transform.enginfo:eu-repo/semantics/closedAccessFractional Kinetic EquationFree-Electron Laser EquationWeighted Hilfer-Prabhakar Fractional DerivativeWeighted Laplace TransformconferenceObject6665368