A novel operational matrix method for solving singularly perturbed boundary value problems of fractional multi-order

In this paper, we will consider a wide class of singularly perturbed problems described by the differential equation of fractional multi-order with small parameter multiplying the highest derivative and the appropriate boundary conditions. We construct the linear B-spline operational matrix of fractional derivative in the Caputo sense and introduce a new operational method to solve the mentioned problems. The main characteristic behind this method is that it converts such problems to a system of algebraic equations and overcomes the difficulty and computational complexity induced by the problem. Some illustrative examples are included to demonstrate the validity and applicability of the method.