Department of Mathematics and Computer Science, University of Bonab, Bonab, Iran
10.22034/jdgaa.2025.721505
چکیده
In this paper, the numerical solution of the initial-value problem involving the time-fractional diffusion problem in the Caputo sense can be express as a series of the shifted Vieta-Fibonacci polynomials with unknown coefficients. Next, by making use of the collocation points and the relations between their coefficients via the boundary conditions, the recent problem is reduced to a system of fractional ordinary differential equations (SFODEs) with initial conditions. Then, utilizing the residual power series method (RPSM) on SFODEs, the analytic approximate solution can be achieved. To illustrate the simplicity and accuracy of the proposed method, some numerical examples are considered.
Sajjadmanesh,Mojtaba . (1403). The solution of the time-fractional diffusion equation by the Vieta–Fibonacci collocation and residual power series methods. (e721505). مجله هندسه دیفرانسیل، کاربردها و جنبهها, 2(1), e721505 doi: 10.22034/jdgaa.2025.721505
MLA
Sajjadmanesh,Mojtaba . "The solution of the time-fractional diffusion equation by the Vieta–Fibonacci collocation and residual power series methods" .e721505 , مجله هندسه دیفرانسیل، کاربردها و جنبهها, 2, 1, 1403, e721505. doi: 10.22034/jdgaa.2025.721505
HARVARD
Sajjadmanesh Mojtaba. (1403). 'The solution of the time-fractional diffusion equation by the Vieta–Fibonacci collocation and residual power series methods', مجله هندسه دیفرانسیل، کاربردها و جنبهها, 2(1), e721505. doi: 10.22034/jdgaa.2025.721505
CHICAGO
Mojtaba Sajjadmanesh, "The solution of the time-fractional diffusion equation by the Vieta–Fibonacci collocation and residual power series methods," مجله هندسه دیفرانسیل، کاربردها و جنبهها, 2 1 (1403): e721505, doi: 10.22034/jdgaa.2025.721505
VANCOUVER
Sajjadmanesh Mojtaba. The solution of the time-fractional diffusion equation by the Vieta–Fibonacci collocation and residual power series methods. JDGAA, 1403; 2(1): e721505. doi: 10.22034/jdgaa.2025.721505
مجله هندسه دیفرانسیل، کاربردها و جنبهها