A Numerical Scheme for Solving Nonlinear Fractional Volterra Integro-Dierential Equations

In this paper, a Bernoulli pseudo-spectral method for solving nonlinear fractional Volterra integro-dierential equations is considered. First existence of a unique solution for the problem under study is proved. Then the Caputo fractional derivative and Riemman-Liouville fractional integral properties are employed to derive a new approximate formula for unknown function of the problem. The suggested technique transforms this type of equations to the solution of a system of algebraic equations. In the next step, the error analysis of the proposed method is investigated. Finally, the technique is applied to some problems to show its validity and applicability.