Advanced Methods for Conformable Time-Fractional Differential Equations: Logarithmic Non-Polynomial Splines
Majeed A. Yousif,
Ravi P. Agarwal,
Pshtiwan Othman Mohammed,
Alina Alb Lupas,
Rashid Jan,
Nejmeddine Chorfi
Affiliations
Majeed A. Yousif
Department of Mathematics, College of Education, University of Zakho, Duhok 42001, Iraq
Ravi P. Agarwal
Department of Mathematics and Systems Engineering, Florida Institute of Technology, Melbourne, FL 32901, USA
Pshtiwan Othman Mohammed
Department of Mathematics, College of Education, University of Sulaimani, Sulaimani 46001, Iraq
Alina Alb Lupas
Department of Mathematics and Computer Science, University of Oradea, 410087 Oradea, Romania
Rashid Jan
Institute of Energy Infrastructure (IEI), Department of Civil Engineering, College of Engineering, Universiti Tenaga Nasional (UNITEN), Putrajaya Campus, Jalan IKRAM-UNITEN, Kajang 43000, Malaysia
Nejmeddine Chorfi
Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
In this study, we present a numerical method named the logarithmic non-polynomial spline method. This method combines conformable derivative, finite difference, and non-polynomial spline techniques to solve the nonlinear inhomogeneous time-fractional Burgers–Huxley equation. The developed numerical scheme is characterized by a sixth-order convergence and conditional stability. The accuracy of the method is demonstrated with 3D mesh plots, while the effects of time and fractional order are shown in 2D plots. Comparative evaluations with the cubic B-spline collocation method are provided. To illustrate the suitability and effectiveness of the proposed method, two examples are tested, with the results are evaluated using L2 and L∞ norms.
