The solution of the time-fractional diffusion equation by the Vieta–Fibonacci collocation and residual power series methods

Sajjadmanesh, Mojtaba

doi:10.22034/jdgaa.2025.721505

The solution of the time-fractional diffusion equation by the Vieta–Fibonacci collocation and residual power series methods

Document Type : Original Article

Author

Mojtaba Sajjadmanesh

Department of Mathematics and Computer Science, University of Bonab, Bonab, Iran

10.22034/jdgaa.2025.721505

Abstract

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.

Keywords

Time -fractional diffusion equation

Caputo fractional derivative

Vieta-Fibonacci polynomials

residual power series method