Numerical solution of nonlinear mixed Fredholm-Volterra integro-differential equations of fractional order by Bernoulli wavelets

In this paper, a numerical method for solving a class of nonlinear mixed Fredholm-Volterra integro-differential equations of fractional order is presented. The method is based upon Bernoulli wavelets approximations. The operational matrix of fractional order integration for Bernoulli wavelets is utilized to reduce the solution of the nonlinear fractional integro-differential equations to system of algebraic equations. Illustrative examples are included to demonstrate the efficiency and accuracy of the method.

Keywords:

Bernoulli wavelets , fractional calculus , Fredholm-Volterra integro-differential equations , Caputo derivative , Operational matrix