Elzaki变换及其在分数阶自由电子激光方程中的应用

Pub Date : 2019-12-01 DOI:10.2478/ausm-2019-0030

Yudhveer Singh, Vinod Gill, Sunil Kundu, Devendra Kumar

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引用次数: 12

摘要

本文研究了Elzaki变换及其在含Hilfer-Prabhakar分数阶导数的自由电子激光方程中的应用。导出了Hilfer-Prabhakar导数的Elzaki变换公式及其正则化形式。用Mittag-Leffler型函数给出了包含分数阶Hilfer-Prabhakar分数阶导数的自由电子激光方程的解。在此基础上，讨论了广义Hilfer-Prabhakar导数在线性偏微分方程中的应用，以及一些数学物理问题。

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On the Elzaki transform and its applications in fractional free electron laser equation

Abstract This article is devoted to study Elzaki transform and its applications in Free Electron Laser equation involving Hilfer-Prabhakar fractional derivative. We derive formula of Elzaki transform for Hilfer–Prabhakar derivative and its regularized version. The solution of Free Electron Laser equation involving Hilfer-Prabhakar fractional derivative of fractional order is presented in terms of Mittag-Leffler type function. Furthermore, we find the application of the generalized Hilfer-Prabhakar derivative in linear partial differential equation and some problems of Mathematical Physics.

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