A numerical study of nonlinear fractional order partial integro-differential equation with a weakly singular kernel

Tayyaba Akram; Zeeshan Ali; Faranak Rabiei; Kamal Shah; Poom Kumam

doi:10.3390/fractalfract5030085

A numerical study of nonlinear fractional order partial integro-differential equation with a weakly singular kernel

Tayyaba Akram, Zeeshan Ali, Faranak Rabiei, Kamal Shah, Poom Kumam

Malaysia Sch of Engineering

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

3 Citations (Scopus)

Abstract

Fractional differential equations can present the physical pathways with the storage and inherited properties due to the memory factor of fractional order. The purpose of this work is to interpret the collocation approach for tackling the fractional partial integro-differential equation (FPIDE) by employing the extended cubic B-spline (ECBS). To determine the time approximation, we utilize the Caputo approach. The stability and convergence analysis have also been analyzed. The efficiency and reliability of the suggested technique are demonstrated by two numerical applications, which support the theoretical results and the effectiveness of the implemented algorithm.

Original language	English
Article number	85
Number of pages	15
Journal	Fractal and Fractional
Volume	5
Issue number	3
DOIs	https://doi.org/10.3390/fractalfract5030085
Publication status	Published - Sep 2021

Keywords

B-spline
Collocation method
Fractional partial integro-differential equation

Access to Document

10.3390/fractalfract5030085Licence: CC BY

361623669-oaFinal published version, 1.8 MBLicence: CC BY

Cite this

@article{966795ea88fc44f4962326192548b876,

title = "A numerical study of nonlinear fractional order partial integro-differential equation with a weakly singular kernel",

abstract = "Fractional differential equations can present the physical pathways with the storage and inherited properties due to the memory factor of fractional order. The purpose of this work is to interpret the collocation approach for tackling the fractional partial integro-differential equation (FPIDE) by employing the extended cubic B-spline (ECBS). To determine the time approximation, we utilize the Caputo approach. The stability and convergence analysis have also been analyzed. The efficiency and reliability of the suggested technique are demonstrated by two numerical applications, which support the theoretical results and the effectiveness of the implemented algorithm.",

keywords = "B-spline, Collocation method, Fractional partial integro-differential equation",

author = "Tayyaba Akram and Zeeshan Ali and Faranak Rabiei and Kamal Shah and Poom Kumam",

note = "Funding Information: Acknowledgments: The authors acknowledge the financial support provided by the Center of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT. Publisher Copyright: {\textcopyright} 2021 by the authors. Licensee MDPI, Basel, Switzerland.",

year = "2021",

month = sep,

doi = "10.3390/fractalfract5030085",

language = "English",

volume = "5",

journal = "Fractal and Fractional",

issn = "2504-3110",

publisher = "MDPI AG",

number = "3",

}

TY - JOUR

T1 - A numerical study of nonlinear fractional order partial integro-differential equation with a weakly singular kernel

AU - Akram, Tayyaba

AU - Ali, Zeeshan

AU - Rabiei, Faranak

AU - Shah, Kamal

AU - Kumam, Poom

N1 - Funding Information: Acknowledgments: The authors acknowledge the financial support provided by the Center of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT. Publisher Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland.

PY - 2021/9

Y1 - 2021/9

N2 - Fractional differential equations can present the physical pathways with the storage and inherited properties due to the memory factor of fractional order. The purpose of this work is to interpret the collocation approach for tackling the fractional partial integro-differential equation (FPIDE) by employing the extended cubic B-spline (ECBS). To determine the time approximation, we utilize the Caputo approach. The stability and convergence analysis have also been analyzed. The efficiency and reliability of the suggested technique are demonstrated by two numerical applications, which support the theoretical results and the effectiveness of the implemented algorithm.

AB - Fractional differential equations can present the physical pathways with the storage and inherited properties due to the memory factor of fractional order. The purpose of this work is to interpret the collocation approach for tackling the fractional partial integro-differential equation (FPIDE) by employing the extended cubic B-spline (ECBS). To determine the time approximation, we utilize the Caputo approach. The stability and convergence analysis have also been analyzed. The efficiency and reliability of the suggested technique are demonstrated by two numerical applications, which support the theoretical results and the effectiveness of the implemented algorithm.

KW - B-spline

KW - Collocation method

KW - Fractional partial integro-differential equation

UR - http://www.scopus.com/inward/record.url?scp=85112281186&partnerID=8YFLogxK

U2 - 10.3390/fractalfract5030085

DO - 10.3390/fractalfract5030085

M3 - Article

AN - SCOPUS:85112281186

VL - 5

JO - Fractal and Fractional

JF - Fractal and Fractional

SN - 2504-3110

IS - 3

M1 - 85

ER -

A numerical study of nonlinear fractional order partial integro-differential equation with a weakly singular kernel

Abstract

Keywords

Access to Document

Other files and links

Cite this