Fractional-order generalized Taylor wavelet method for systems of nonlinear fractional differential equations with application to human respiratory syncytial virus infection

We give a novel method to solve systems of nonlinear fractional differential equations (NFDEs). We first introduce a new class of basis functions called fractional-order generalized Taylor wavelets. The Riemann–Liouville fractional integral operator, of the fractional-order generalized Taylor wavelets, is determined. An exact formula for this operator will be obtained by using the regularized beta function. By applying this exact formula we reduce the given system of NFDEs to a system of algebraic equations. The method is applied to the fractional models in human respiratory syncytial virus infection. We also give numerical examples to show the effectiveness and high accuracy of the present method.