# Analytical treatment of two-dimensional fractional Helmholtz equations

Salah Abuasad, Khaled Moaddy, Ishak Hashim

Research output: Contribution to journalArticle

4 Citations (Scopus)

### Abstract

In this paper, we propose a semi numerical-analytical method, called Fractional Reduced Differential Transform Method (FRDTM), for finding exact and approximate solutions of fractional Helmholtz equation with appropriate initial conditions. The fractional derivatives are demonstrated in the Caputo sense. The solutions are given in the form of series with easily computable terms, then with the help of Mittag-Leffler function, we find the exact solutions of the fractional Helmholtz equations. Three examples are given to demonstrate the applicability of FRDTM.

Original language English Journal of King Saud University - Science https://doi.org/10.1016/j.jksus.2018.02.002 Accepted/In press - 1 Jan 2018

### Fingerprint

Helmholtz equations

### Keywords

• Caputo derivative
• Fractional calculus
• Fractional reduced differential transform method
• Helmholtz equation
• Mittag-Leffler function

• General

### Cite this

Analytical treatment of two-dimensional fractional Helmholtz equations. / Abuasad, Salah; Moaddy, Khaled; Hashim, Ishak.

In: Journal of King Saud University - Science, 01.01.2018.

Research output: Contribution to journalArticle

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AB - In this paper, we propose a semi numerical-analytical method, called Fractional Reduced Differential Transform Method (FRDTM), for finding exact and approximate solutions of fractional Helmholtz equation with appropriate initial conditions. The fractional derivatives are demonstrated in the Caputo sense. The solutions are given in the form of series with easily computable terms, then with the help of Mittag-Leffler function, we find the exact solutions of the fractional Helmholtz equations. Three examples are given to demonstrate the applicability of FRDTM.

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