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DEVELOPMENT AND ANALYSIS OF NEW APPROXIMATION OF EXTENDED CUBIC B-SPLINE TO THE NONLINEAR TIME FRACTIONAL KLEIN–GORDON EQUATION

TAYYABA AKRAM

School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia

E-mail Address: tayyaba.akram2020@gmail.com

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MUHAMMAD ABBAS

Informetrics Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam

Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

Department of Mathematics, University of Sargodha, 40100 Sargodha, Pakistan

E-mail Address: muhammadabbas@tdtu.edu.vn

Corresponding authors.

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MUHAMMAD BILAL RIAZ

Department of Mathematics, University of Management and Technology, C-II Johar Town Lahore, Pakistan

Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, South Africa

E-mail Address: bilalsehole@gmail.com

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AHMAD IZANI ISMAIL

School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia

E-mail Address: ahmad_izani@usm.my

Corresponding authors.

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, and

NORHASHIDAH MOHD. ALI

School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia

E-mail Address: shidah_ali@usm.my

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https://doi.org/10.1142/S0218348X20400393Cited by:14 (Source: Crossref)

This article is part of the issue:

Special Issue on Fractal and Fractional with Applications to Nature
Guest Editors: Abdon Atangana, Emile Franc Goufo Ndongmo, José Francisco Gómez Aguilar, Muhammad Altaf Khan and Ilknur Koca

Abstract

A new extended cubic B-spline (ECBS) approximation is formulated, analyzed and applied to obtain the numerical solution of the time fractional Klein–Gordon equation. The temporal fractional derivative is estimated using Caputo’s discretization and the space derivative is discretized by ECBS basis functions. A combination of Caputo’s fractional derivative and the new approximation of ECBS together with $𝜃$ -weighted scheme is utilized to obtain the solution. The method is shown to be unconditionally stable and convergent. Numerical examples indicate that the obtained results compare well with other numerical results available in the literature.

Keywords:

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Vol. 28, No. 08

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History

Received 19 December 2019

Accepted 23 February 2020

Published: September 18, 2020

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This is an Open Access article in the “Special Issue on Fractal and Fractional with Applications to Nature” published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC BY) License which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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DEVELOPMENT AND ANALYSIS OF NEW APPROXIMATION OF EXTENDED CUBIC B-SPLINE TO THE NONLINEAR TIME FRACTIONAL KLEIN–GORDON EQUATION

Abstract

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