Solving a higher-dimensional time-fractional diffusion equation via the fractional reduced differential transform method

Salah Abuasad; Saleh Alshammari; Adil Al-Rabtah; Ishak Hashim

doi:10.3390/fractalfract5040168

Solving a higher-dimensional time-fractional diffusion equation via the fractional reduced differential transform method

Salah Abuasad
, Saleh Alshammari
, Adil Al-Rabtah
, Ishak Hashim

Universiti Kebangsaan Malaysia
University of Hail
University of Mutah

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

6 Scopus citations

Abstract

In this study, exact and approximate solutions of higher-dimensional time-fractional diffusion equations were obtained using a relatively new method, the fractional reduced differential transform method (FRDTM). The exact solutions can be found with the benefit of a special function, and we applied Caputo fractional derivatives in this method. The numerical results and graphical representations specified that the proposed method is very effective for solving fractional diffusion equations in higher dimensions.

Original language	English
Article number	168
Journal	Fractal and Fractional
Volume	5
Issue number	4
DOIs	https://doi.org/10.3390/fractalfract5040168
State	Published - Dec 2021
Externally published	Yes

Keywords

Caputo derivative
Fractional calculus
Fractional reduced differential transform method
Time-fractional diffusion equations

Access to Document

10.3390/fractalfract5040168

Cite this

@article{7c601816784147ab83571d94da352e01,

title = "Solving a higher-dimensional time-fractional diffusion equation via the fractional reduced differential transform method",

abstract = "In this study, exact and approximate solutions of higher-dimensional time-fractional diffusion equations were obtained using a relatively new method, the fractional reduced differential transform method (FRDTM). The exact solutions can be found with the benefit of a special function, and we applied Caputo fractional derivatives in this method. The numerical results and graphical representations specified that the proposed method is very effective for solving fractional diffusion equations in higher dimensions.",

keywords = "Caputo derivative, Fractional calculus, Fractional reduced differential transform method, Time-fractional diffusion equations",

author = "Salah Abuasad and Saleh Alshammari and Adil Al-Rabtah and Ishak Hashim",

note = "Publisher Copyright: {\textcopyright} 2021 by the authors. Licensee MDPI, Basel, Switzerland.",

year = "2021",

month = dec,

doi = "10.3390/fractalfract5040168",

language = "English",

volume = "5",

journal = "Fractal and Fractional",

issn = "2504-3110",

publisher = "Multidisciplinary Digital Publishing Institute (MDPI)",

number = "4",

}

TY - JOUR

T1 - Solving a higher-dimensional time-fractional diffusion equation via the fractional reduced differential transform method

AU - Abuasad, Salah

AU - Alshammari, Saleh

AU - Al-Rabtah, Adil

AU - Hashim, Ishak

PY - 2021/12

Y1 - 2021/12

N2 - In this study, exact and approximate solutions of higher-dimensional time-fractional diffusion equations were obtained using a relatively new method, the fractional reduced differential transform method (FRDTM). The exact solutions can be found with the benefit of a special function, and we applied Caputo fractional derivatives in this method. The numerical results and graphical representations specified that the proposed method is very effective for solving fractional diffusion equations in higher dimensions.

AB - In this study, exact and approximate solutions of higher-dimensional time-fractional diffusion equations were obtained using a relatively new method, the fractional reduced differential transform method (FRDTM). The exact solutions can be found with the benefit of a special function, and we applied Caputo fractional derivatives in this method. The numerical results and graphical representations specified that the proposed method is very effective for solving fractional diffusion equations in higher dimensions.

KW - Caputo derivative

KW - Fractional calculus

KW - Fractional reduced differential transform method

KW - Time-fractional diffusion equations

UR - https://www.scopus.com/pages/publications/85118411923

U2 - 10.3390/fractalfract5040168

DO - 10.3390/fractalfract5040168

M3 - Article

AN - SCOPUS:85118411923

SN - 2504-3110

VL - 5

JO - Fractal and Fractional

JF - Fractal and Fractional

IS - 4

M1 - 168

ER -

Solving a higher-dimensional time-fractional diffusion equation via the fractional reduced differential transform method

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this