Numerical solution of nonlinear Volterra integro-differential equations of fractional order by the reproducing kernel method

Fractional calculus is a extension of derivatives and integrals to non-integer orders. It has been used widely to model scientific and engineering problems. In this article, the reproducing kernel theory is applied to solve a kind of nonlinear fractional order Volterra integro-differential equation. The fraction derivatives are described in Caputo sense. In order to solve this kind of equation, we discuss and derive the approximate solution in the form of series with easily computable terms in the reproducing kernel space, by introducing a simple algorithm to implement this process. Some numerical examples are given to demonstrate the validity and applicability of the technique.