ANALYSIS AND IMPLEMENTATION OF NUMERICAL SCHEME FOR THE VARIABLE-ORDER FRACTIONAL MODIFIED SUB-DIFFUSION EQUATION

Umair Ali; Muhammad Naeem; Farah Aini Abdullah; Miao Kun Wang; Fouad Mohammad Salama

doi:10.1142/S0218348X22402538

ANALYSIS AND IMPLEMENTATION OF NUMERICAL SCHEME FOR THE VARIABLE-ORDER FRACTIONAL MODIFIED SUB-DIFFUSION EQUATION

Umair Ali, Muhammad Naeem, Farah Aini Abdullah, Miao Kun Wang^*, Fouad Mohammad Salama

^*Corresponding author for this work

Department of Mathematics

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

7 Scopus citations

Abstract

This paper addresses the numerical study of variable-order fractional differential equation based on finite-difference method. We utilize the implicit numerical scheme to find out the solution of two-dimensional variable-order fractional modified sub-diffusion equation. The discretized form of the variable-order Riemann-Liouville differential operator is used for the fractional variable-order differential operator. The theoretical analysis including for stability and convergence is made by the von Neumann method. The analysis confirmed that the proposed scheme is unconditionally stable and convergent. Numerical simulation results are given to validate the theoretical analysis as well as demonstrate the accuracy and efficiency of the implicit scheme.

Original language	English
Article number	2240253
Journal	Fractals
Volume	30
Issue number	10
DOIs	https://doi.org/10.1142/S0218348X22402538
State	Published - 1 Dec 2022

Bibliographical note

Publisher Copyright:
© 2022 The Author(s).

Keywords

Convergence
Implicit Scheme
Stability
Variable-Order Fractional Modified Sub-Diffusion Equation

ASJC Scopus subject areas

Modeling and Simulation
Geometry and Topology
Applied Mathematics

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10.1142/S0218348X22402538

Cite this

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title = "ANALYSIS AND IMPLEMENTATION OF NUMERICAL SCHEME FOR THE VARIABLE-ORDER FRACTIONAL MODIFIED SUB-DIFFUSION EQUATION",

abstract = "This paper addresses the numerical study of variable-order fractional differential equation based on finite-difference method. We utilize the implicit numerical scheme to find out the solution of two-dimensional variable-order fractional modified sub-diffusion equation. The discretized form of the variable-order Riemann-Liouville differential operator is used for the fractional variable-order differential operator. The theoretical analysis including for stability and convergence is made by the von Neumann method. The analysis confirmed that the proposed scheme is unconditionally stable and convergent. Numerical simulation results are given to validate the theoretical analysis as well as demonstrate the accuracy and efficiency of the implicit scheme.",

keywords = "Convergence, Implicit Scheme, Stability, Variable-Order Fractional Modified Sub-Diffusion Equation",

author = "Umair Ali and Muhammad Naeem and Abdullah, \{Farah Aini\} and Wang, \{Miao Kun\} and Salama, \{Fouad Mohammad\}",

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T1 - ANALYSIS AND IMPLEMENTATION OF NUMERICAL SCHEME FOR THE VARIABLE-ORDER FRACTIONAL MODIFIED SUB-DIFFUSION EQUATION

AU - Ali, Umair

AU - Naeem, Muhammad

AU - Abdullah, Farah Aini

AU - Wang, Miao Kun

AU - Salama, Fouad Mohammad

PY - 2022/12/1

Y1 - 2022/12/1

N2 - This paper addresses the numerical study of variable-order fractional differential equation based on finite-difference method. We utilize the implicit numerical scheme to find out the solution of two-dimensional variable-order fractional modified sub-diffusion equation. The discretized form of the variable-order Riemann-Liouville differential operator is used for the fractional variable-order differential operator. The theoretical analysis including for stability and convergence is made by the von Neumann method. The analysis confirmed that the proposed scheme is unconditionally stable and convergent. Numerical simulation results are given to validate the theoretical analysis as well as demonstrate the accuracy and efficiency of the implicit scheme.

AB - This paper addresses the numerical study of variable-order fractional differential equation based on finite-difference method. We utilize the implicit numerical scheme to find out the solution of two-dimensional variable-order fractional modified sub-diffusion equation. The discretized form of the variable-order Riemann-Liouville differential operator is used for the fractional variable-order differential operator. The theoretical analysis including for stability and convergence is made by the von Neumann method. The analysis confirmed that the proposed scheme is unconditionally stable and convergent. Numerical simulation results are given to validate the theoretical analysis as well as demonstrate the accuracy and efficiency of the implicit scheme.

KW - Convergence

KW - Implicit Scheme

KW - Stability

KW - Variable-Order Fractional Modified Sub-Diffusion Equation

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DO - 10.1142/S0218348X22402538

M3 - Article

AN - SCOPUS:85143620892

SN - 0218-348X

VL - 30

JO - Fractals

JF - Fractals

IS - 10

M1 - 2240253

ER -

ANALYSIS AND IMPLEMENTATION OF NUMERICAL SCHEME FOR THE VARIABLE-ORDER FRACTIONAL MODIFIED SUB-DIFFUSION EQUATION

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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