B-spline method for solving fractional delay differential equations

In this paper, we used the fractional collocation method based on the B-spline basis to derive the numerical solutions for a special form of fractional delay differential equations (DFDEs). The fractional derivative used is defined in the sense of Caputo. So, we can represent the DFDE under consideration into a matrix form that can be solved using matrix operations and tools from linear algebra. As a result, we get algebraic equations with unknown coefficients that can be solved efficiently using a computer algorithm. To illustrate the validity and efficiency of the method, exact and approximate solutions are compared, and absolute errors are found using an example. The numerical results, which are backed up by simulation, reveal that the absolute error is very small and that the approach is extremely efficient.