Journal
FRACTAL AND FRACTIONAL
Volume 6, Issue 2, Pages -Publisher
MDPI
DOI: 10.3390/fractalfract6020050
Keywords
cubic B-splines; trigonometric cubic B-splines; extended cubic B-splines; Caputo-Fabrizio derivative; Cattaneo equation
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Funding
- Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia
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This study numerically addresses the time fractional Cattaneo equation involving Caputo-Fabrizio derivative using spline-based numerical techniques. The proposed schemes are stable and convergent, and the efficiency of the schemes is demonstrated through numerical studies.
This study focuses on numerically addressing the time fractional Cattaneo equation involving Caputo-Fabrizio derivative using spline-based numerical techniques. The splines used are the cubic B-splines, trigonometric cubic B-splines and extended cubic B-splines. The space derivative is approximated using B-splines basis functions, Caputo-Fabrizio derivative is discretized, using a finite difference approach. The techniques are also put through a stability analysis to verify that the errors do not pile up. The proposed scheme's convergence analysis is also explored. The key advantage of the schemes is that the approximation solution is produced as a smooth piecewise continuous function, allowing us to approximate a solution at any place in the domain of interest. A numerical study is performed using various splines, and the outcomes are compared to demonstrate the efficiency of the proposed schemes.
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