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In this paper, a new numerical method for solving nonlinear fractional integro-differential equations is presented. The method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The Riemann–Liouville fractional integral operator for hybrid functions is given. This operator is then utilized to reduce the solution of the nonlinear fractional integro-differential equations to a system of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique. [ABSTRACT FROM AUTHOR]

A method for the solution of Volterra integro-differential equations by using single-term Walsh series is presented. Properties of single-term Walsh series are utilized to reduce the computation of Volterra integro-differential equations to some algebraic equations. The method is computationally attractive, and applications are demonstrated through illustrative examples. [Copyright &y& Elsevier]