SOLVING TIME-FRACTIONAL FISHER MODELS BY NON-POLYNOMIAL SPLINES IN TERMS OF LOGARITHMIC DERIVATIVES

Hari Mohan Srivastava, Majeed A. Yousif, Pshtiwan Othman Mohammed, Thabet Abdeljawad, Dumitru Baleanu and Nejmeddine Chorfi
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Hari Mohan Srivastava: Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada
Majeed A. Yousif: Department of Mathematics, College of Education, University of Zakho, Duhok 42001, Iraq
Pshtiwan Othman Mohammed: Research and Development Center, University of Sulaimani, Sulaymaniyah 46001, Iraq4Research Center, University of Halabja, Halabja 46018, Iraq
Thabet Abdeljawad: Department of Mathematics and Sciences, Prince Sultan University, P. O. Box 66833, Riyadh 11586, Saudi Arabia6Department of Medical Research, China Medical University, Taichung, 40402, Taiwan7Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Garankuwa, Medusa, 0204, South Africa8Center for Applied Mathematics and Bioinformatics (CAMB), Gulf University for Science and Technology, Hawally, Kuwait
Dumitru Baleanu: Department of Computer Science and Mathematics, Lebanese American University, Beirut 11022801, Lebanon
Nejmeddine Chorfi: 0Department of Mathematics, College of Science, King Saud University, P. O. Box 2455, Riyadh 11451, Saudi Arabia

FRACTALS (fractals), 2025, vol. 33, issue 08, 1-10

Abstract: This paper introduces a novel numerical approach, the logarithmic non-polynomial spline method (LNPSM), leveraging a non-polynomial spline function with logarithmic terms to solve the conformable time-fractional Fisher (TFF) equation. The developed scheme achieves six-order convergence, derived through truncation error analysis and the Taylor series expansion. Stability is ensured under conditional constraints verified by von Neumann stability analysis. The method’s accuracy is demonstrated through two test examples, with results presented in comparison tables alongside cubic B-spline and Caputo non-polynomial spline methods, evaluated by norm errors. Additionally, graphical representations, including 2D and 3D plots, further illustrate the effectiveness of LNPSM. The findings indicate that LNPSM is a suitable and robust tool for solving time-fractional differential equations.

Keywords: Natural Logarithmic Non-Polynomial Splines; Time-Fractional Fisher Equation; Stability Analysis; Conformable Derivative (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25401425

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