학술논문
Some Integral Transform Results for Hilfer–Prabhakar Fractional Derivative and Analysis of Free-Electron Laser Equation
Document Type
Original Paper
Source
Iranian Journal of Science. 47(4):1333-1342
Subject
Language
English
ISSN
2731-8095
2731-8109
2731-8109
Abstract
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.