An Efficient and Simple Algorithm for Solving Fractional Order Differential Equations

Abstract It is presents and discuss an algorithm to generate the numerical solution of fractional differential equations in the form: Dα ∗ x(t) = f(t, x(t)), x(0) = x0, with α ∈ R +, where Dα ∗ x(t) is the derivative of order α in the sense of Caputo of the function x(t). The algorithm is based on a variable change that suppresses the fractional integral kernel that enables us to establish a simple first order quadrature for the operator of fractional integration. We extend the result to a wider class of fractional differential equations, and conclude the article with numerical examples that show the effectiveness and convenience of the application of our algorithm.