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On Weighted Fractional Operators with Applications to Mathematical Models Arising in Physics

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Advances in Mathematical Modelling, Applied Analysis and Computation (ICMMAAC 2022)

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 666))

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Abstract

In 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.

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Correspondence to Muhammad Samraiz .

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Samraiz, M., Umer, M., Naheed, S., Baleanu, D. (2023). On Weighted Fractional Operators with Applications to Mathematical Models Arising in Physics. In: Singh, J., Anastassiou, G.A., Baleanu, D., Kumar, D. (eds) Advances in Mathematical Modelling, Applied Analysis and Computation . ICMMAAC 2022. Lecture Notes in Networks and Systems, vol 666. Springer, Cham. https://doi.org/10.1007/978-3-031-29959-9_3

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  • DOI: https://doi.org/10.1007/978-3-031-29959-9_3

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