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Redefined Extended Cubic B-Spline Functions for Numerical Solution of Time-Fractional Telegraph Equation

Muhammad Amin1, Muhammad Abbas2,*, Dumitru Baleanu3,4,5, Muhammad Kashif Iqbal6, Muhammad Bilal Riaz7

1 Department of Mathematics, National College of Business Administration & Economics, Lahore, 54660, Pakistan
2 Department of Mathematics, University of Sargodha, Sargodha, 40100, Pakistan
3 Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, Ankara, 06530, Turkey
4 Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan
5 Institute of Space-Sciences, Bucharest, 077125, Romania
6 Department of Mathematics, Government College University, Faisalabad, 38000, Pakistan
7 Department of Mathematics, University of Management and Technology, Lahore, 54700, Pakistan

* Corresponding Author: Muhammad Abbas. Email:

(This article belongs to this Special Issue: Modeling Real World Problems with Mathematics)

Computer Modeling in Engineering & Sciences 2021, 127(1), 361-384.


This work is concerned with the application of a redefined set of extended uniform cubic B-spline (RECBS) functions for the numerical treatment of time-fractional Telegraph equation. The presented technique engages finite difference formulation for discretizing the Caputo time-fractional derivatives and RECBS functions to interpolate the solution curve along the spatial grid. Stability analysis of the scheme is provided to ensure that the errors do not amplify during the execution of the numerical procedure. The derivation of uniform convergence has also been presented. Some computational experiments are executed to verify the theoretical considerations. Numerical results are compared with the existing schemes and it is concluded that the present scheme returns superior outcomes on the topic.


Cite This Article

Amin, M., Abbas, M., Baleanu, D., Iqbal, M. K., Riaz, M. B. (2021). Redefined Extended Cubic B-Spline Functions for Numerical Solution of Time-Fractional Telegraph Equation. CMES-Computer Modeling in Engineering & Sciences, 127(1), 361–384.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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