MEMORY EFFECT ANALYSIS USING PIECEWISE CUBIC B-SPLINE OF TIME FRACTIONAL DIFFUSION EQUATION

Madiha Shafiq; Farah Aini Abdullah; Muhammad Abbas; Ahmed Sm Alzaidi; Muhammad Riaz

doi:10.1142/s0218348x22402708

MEMORY EFFECT ANALYSIS USING PIECEWISE CUBIC B-SPLINE OF TIME FRACTIONAL DIFFUSION EQUATION

Abstract

The purpose of this work is to study the memory effect analysis of Caputo–Fabrizio time fractional diffusion equation by means of cubic B-spline functions. The Caputo–Fabrizio interpretation of fractional derivative involves a non-singular kernel that permits to describe some class of material heterogeneities and the effect of memory more effectively. The proposed numerical technique relies on finite difference approach and cubic B-spline functions for discretization along temporal and spatial grids, respectively. To ensure that the error does not amplify during computational process, stability analysis is performed. The described algorithm is second-order convergent along time and space directions. The computational competence of the scheme is tested through some numerical examples. The results reveal that the current scheme is reasonably efficient and reliable to be used for solving the subject problem.

Citations

6

CrossRef
0

Web of Science
6

Scopus

Authors (5)

Cite as

Full text

download paper

downloaded 21 times

Publication version: Accepted or Published Version
DOI:: Digital Object Identifier (open in new tab) 10.1142/S0218348X22402708
License: open in new tab

Keywords

Details

Category:

Articles

Type:

artykuły w czasopismach

Published in:

FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY no. 30,
ISSN: 0218-348X

Language:

English

Publication year:

2022

Bibliographic description:

Shafiq M., Abdullah F. A., Abbas M., Sm Alzaidi A., Riaz M.: MEMORY EFFECT ANALYSIS USING PIECEWISE CUBIC B-SPLINE OF TIME FRACTIONAL DIFFUSION EQUATION// FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY -Vol. 30,iss. 08 (2022),

DOI: