Hilfer-Prabhakar分数阶导数的一些积分变换结果及自由电子激光方程的分析

IF 1.4 4区综合性期刊 Q2 MULTIDISCIPLINARY SCIENCES Iranian Journal of Science and Technology, Transactions A: Science Pub Date : 2023-07-25 DOI:10.1007/s40995-023-01493-9

Ved Prakash Dubey, Jagdev Singh, Sarvesh Dubey, Devendra Kumar

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引用次数: 4

摘要

本文计算了Prabhakar积分、Hilfer-Prabhakar (HP)分数阶导数和HP分数阶导数的正则化Caputo形式的自然变换。在此基础上，研究了分数阶自由电子激光方程和分数阶柯西问题的自然变换解法。利用自然变换和傅里叶变换的运算，以广义三参数Mittag-Leffler函数的形式实现了以Hilfer-Prabhakar分数阶导数及其正则Caputo形式建模的Cauchy问题的解。

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Some Integral Transform Results for Hilfer–Prabhakar Fractional Derivative and Analysis of Free-Electron Laser Equation

In this paper, Natural transforms of Prabhakar integral, Hilfer–Prabhakar (HP) fractional derivative and regularized Caputo form of HP fractional derivative (HPFD) are computed. Furthermore, we investigate the solution of a fractional free-electron laser equation and fractional Cauchy problems involving the HPFD via the Natural transform. The solution of Cauchy problems modeled with Hilfer–Prabhakar fractional derivatives and its regularized Caputo version is achieved in the form of generalized three parameter Mittag–Leffler function by operations of Natural and Fourier transforms.

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来源期刊

Iranian Journal of Science and Technology, Transactions A: Science MULTIDISCIPLINARY SCIENCES-

CiteScore

4.00

自引率

5.90%

发文量

122

审稿时长

>12 weeks

期刊介绍： The aim of this journal is to foster the growth of scientific research among Iranian scientists and to provide a medium which brings the fruits of their research to the attention of the world’s scientific community. The journal publishes original research findings – which may be theoretical, experimental or both - reviews, techniques, and comments spanning all subjects in the field of basic sciences, including Physics, Chemistry, Mathematics, Statistics, Biology and Earth Sciences