Explicit Chebyshev Collocation Method for Multi-Order Fractional Nonlinear Boundary Value Problems in Mathematical Chemistry
نویسندگان
1 Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo 11341, Egypt
2 Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt
doi
10.22052/ijmc.2025.256602.1997چکیده
This paper presents a numerical method for solving a class of nonlinear multi-order fractional differential equations using the first-kind Chebyshev polynomials. The proposed approach is based on a collocation framework that incorporates operational matrices of derivatives specifically tailored to the spectral properties of the Chebyshev polynomials on the interval $[0,1]$. Two cases of interest are considered: the classical case with $\nu = 2$ and $\lambda = 1$, and the fractional-order case with $1 < \nu \leq 2$ and $0 < \lambda \leq 1$. To ensure high accuracy, an appropriate set of the shifted Chebyshev basis functions that satisfy the boundary conditions is utilized. The Caputo definition of fractional derivatives is adopted to handle the fractional operators. The resulting nonlinear algebraic system is solved efficiently using Newton’s method. Numerical experiments confirm the proposed method’s efficiency, stability, and accuracy in comparison with existing techniques.
