In the current study, we used Chebyshev’s Pseudospectral Method (CPM), a novel numerical technique, to solve nonlinear third-order Emden–Fowler delay differential (EF-DD) equations numerically. Fractional derivatives are defined by the Caputo operator. These kinds of equations are transformed to the linear or nonlinear algebraic equations by the proposed approach. The numerical outcomes demonstrate the precision and efficiency of the suggested approach. The error analysis shows that the current method is more accurate than any other numerical method currently available. The computational analysis fully confirms the compatibility of the suggested strategy, as demonstrated by a few numerical examples. We present the outcome of the offered method in tables form, which confirms the appropriateness at each point. Additionally, the outcomes of the offered method at various non-integer orders are investigated, demonstrating that the result approaches closer to the accurate solution as a value approaches from non-integer order to an integer order. Additionally, the current study proves some helpful theorems about the convergence and error analysis related to the aforementioned technique. A suggested algorithm can effectively be used to solve other physical issues.
Mashael M. AlBaidani (Sat,) studied this question.