Chebyshev Polynomials of Sixth Kind for Solving Nonlinear Fractional PDEs with Proportional Delay and Its Convergence Analysis. (7th January 2022)

• Record Type: Journal Article
• Authors: Sadri, Khadijeh; Aminikhah, Hossein
• Other Names: Youssri Youssri Hassan Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2022(2022)
• Publication Date: 2022-01-07
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2022/9512048
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : This work devotes to solving a class of delay fractional partial differential equations that arises in physical, biological, medical, and climate models. For this, a numerical scheme is implemented that applies operational matrices to convert the main problem into a system of algebraic equations; then, solving the resultant system leads to an approximate solution. The two-variable Chebyshev polynomials of the sixth kind, as basis functions in the proposed method, are constructed by the one-variable ones, and their operational matrices are derived. Error bounds of approximate solutions and their fractional and classical derivatives are computed. With the aid of these bounds, a bound for the residual function is estimated. Three illustrative examples demonstrate the simplicity and efficiency of the proposed method.