Analytical treatment of two-dimensional fractional Helmholtz equations

Salah Abuasad; Khaled Moaddy; Ishak Hashim

doi:10.1016/j.jksus.2018.02.002

Analytical treatment of two-dimensional fractional Helmholtz equations

Salah Abuasad
, Khaled Moaddy
, Ishak Hashim

King Faisal University
Shaqra University
Universiti Kebangsaan Malaysia

Research output: Contribution to journal › Article › peer-review

26 Scopus citations

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
Pages (from-to)	659-666
Number of pages	8
Journal	Journal of King Saud University - Science
Volume	31
Issue number	4
DOIs	https://doi.org/10.1016/j.jksus.2018.02.002
State	Published - Oct 2019
Externally published	Yes

Keywords

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

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10.1016/j.jksus.2018.02.002

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title = "Analytical treatment of two-dimensional fractional Helmholtz equations",

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.",

keywords = "Caputo derivative, Fractional calculus, Fractional reduced differential transform method, Helmholtz equation, Mittag-Leffler function",

author = "Salah Abuasad and Khaled Moaddy and Ishak Hashim",

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T1 - Analytical treatment of two-dimensional fractional Helmholtz equations

AU - Abuasad, Salah

AU - Moaddy, Khaled

AU - Hashim, Ishak

PY - 2019/10

Y1 - 2019/10

N2 - 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.

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.

KW - Caputo derivative

KW - Fractional calculus

KW - Fractional reduced differential transform method

KW - Helmholtz equation

KW - Mittag-Leffler function

UR - https://www.scopus.com/pages/publications/85042907238

U2 - 10.1016/j.jksus.2018.02.002

DO - 10.1016/j.jksus.2018.02.002

M3 - Article

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SN - 1018-3647

VL - 31

SP - 659

EP - 666

JO - Journal of King Saud University - Science

JF - Journal of King Saud University - Science

IS - 4

ER -

Analytical treatment of two-dimensional fractional Helmholtz equations

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Keywords

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