Integrated Intelligence of Fractional Neural Networks and Sequential Quadratic Programming for Bagley–Torvik Systems Arising in Fluid Mechanics

In this study, an efficient soft computing paradigm is presented for solving Bagley–Torvik systems of fractional order arising in fluid dynamic model for the motion of a rigid plate immersed in a Newtonian fluid using feed-forward fractional artificial neural networks (FrANNs) and sequential quadratic programming (SQP) algorithm. The strength of FrANNs has been utilized to construct an accurate modeling of the equation using approximation theory in mean square error sense. Training of weights of FrANNs is performed with SQP techniques. The designed scheme has been examined on different variants of the systems. The comparative studies of the proposed solutions with available exact as well as reference numerical results demonstrate the worth and effectiveness of the solver. The accuracy, consistency, and complexity are evaluated in depth through results of statistics.