A Comparative B-Spline Collocation Framework for the Caputo Time-Fractional Mobile–Immobile Transport Equation
- 1Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan
- 2Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
Abstract
In this study, we present a novel and efficient computational framework for obtaining approximate solutions of the time-fractional mobile–immobile transport equation, where the temporal derivative is considered in the Caputo sense with order 0<γ≤1. The spatial derivatives are discretized using three different B-spline basis functions, namely cubic B-splines (CuBS), trigonometric cubic B-splines (TCuBS), and extended cubic B-splines (ECuBS), while the time-fractional derivative is approximated through an appropriate finite difference scheme. The theoretical reliability of the proposed schemes is established by conducting stability and convergence analyses. To evaluate the accuracy and computational efficiency of the proposed methods, several numerical experiments are performed. The obtained results demonstrate a strong agreement between the numerical and exact solutions and confirm the effectiveness of the developed schemes. Furthermore, a comparative study of the three B-spline approaches is carried out, highlighting their advantages under different conditions. The proposed schemes provide reliable, accurate, and efficient numerical tools for solving time-fractional mobile–immobile transport equations.
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BibTeX
@article{shafique2026comparative,
title = {{A Comparative B-Spline Collocation Framework for the Caputo Time-Fractional Mobile–Immobile Transport Equation}},
author = {Marryam Shafique and Muhammad Yaseen and Khidir Shaib Mohamed and Muntasir Suhail and Habeeb Ibrahim},
journal = {Fractal and Fractional},
year = {2026},
month = oct,
doi = {10.3390/fractalfract10100698},
url = {https://www.mdpi.com/2504-3110/10/10/698},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - A Comparative B-Spline Collocation Framework for the Caputo Time-Fractional Mobile–Immobile Transport Equation
AU - Marryam Shafique
AU - Muhammad Yaseen
AU - Khidir Shaib Mohamed
AU - Muntasir Suhail
AU - Habeeb Ibrahim
PY - 2026
DA - 2026/10/04
JO - Fractal and Fractional
DO - 10.3390/fractalfract10100698
UR - https://www.mdpi.com/2504-3110/10/10/698
AB - In this study, we present a novel and efficient computational framework for obtaining approximate solutions of the time-fractional mobile–immobile transport equation, where the temporal derivative is considered in the Caputo sense with order 0<γ≤1. The spatial derivatives are discretized using three different B-spline basis functions, namely cubic B-splines (CuBS), trigonometric cubic B-splines (TCuBS), and extended cubic B-splines (ECuBS), while the time-fractional derivative is approximated through an appropriate finite difference scheme. The theoretical reliability of the proposed schemes is established by conducting stability and convergence analyses. To evaluate the accuracy and computational efficiency of the proposed methods, several numerical experiments are performed. The obtained results demonstrate a strong agreement between the numerical and exact solutions and confirm the effectiveness of the developed schemes. Furthermore, a comparative study of the three B-spline approaches is carried out, highlighting their advantages under different conditions. The proposed schemes provide reliable, accurate, and efficient numerical tools for solving time-fractional mobile–immobile transport equations.
SN - 2504-3110
ER -