Uniqueness and approximation of solution for fractional Bagley-Torvik equations with variable coefficients

摘要

The initial value problem for fractional Bagley-Torvik equations is investigated by considering variable coefficients and the fractional order as . Making use of the integration method, a Volterra integral equation of the second kind is obtained. Then the contraction operator theorem in Banach spaces is further used to address the uniqueness of the solution for the obtained Volterra integral equation. A novel numerical method is proposed to find the approximate solution of the given Volterra integral equation. Moreover, the convergence and error estimate of the approximate solution are analysed. Finally, some numerical examples are carried out to show the effectiveness of the proposed method by comparing with the existing ones. The developed method will be helpful for finding a good approximation solution of fractional differential equations in practical applications.