Umer, M.Naheed, S.Baleanu, D.Samraiz, M.2024-01-292025-09-182024-01-292025-09-182023Samraiz, Muhammad;...et.al. "On Weighted Fractional Operators with Applications to Mathematical Models Arising in Physics", Advances in Mathematical Modelling, Applied Analysis and Computation, ICMMAAC 2022, Proceedings, pp.53-68, 2023.97830312995822367-3370https://doi.org/10.1007/978-3-031-29959-9_3https://hdl.handle.net/20.500.12416/13984In 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. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.eninfo:eu-repo/semantics/closedAccessFractional Kinetic EquationFree-Electron Laser EquationWeighted Hilfer-Prabhakar Fractional DerivativeWeighted Laplace TransformConference Object10.1007/978-3-031-29959-9_32-s2.0-85161652769