An Approximate Analytical Method For Fractional Order Gradient-Based Dynamic System Generated By An Optimization Problem

In this paper, an efficient hybrid Laplace homotopy asymptotic method(HLHAM) was applied to obtain an approximate analytic solution for fractional-order gradient-based dynamic system(FOGBDS) generated by non-linear programming equality constrained optimization problems (NLPECOPs). The constrained optimization problem is constructed in form of a non-linear system of fractional differential equations and the solutions of the system, modeled with a Caputo fractional derivative of steepest descent concept are investigated to obtain the minimizing point of the optimization problem. The HLHAM is the hybridization of homotopy analysis method with Laplace transform method, HLHAM enable us to regulate and manage the convergence domain of the series solution by initiating convergence control parameters. We show the impact of hcurve on the convergence of the series solution given by HLHAM by plotting hcurve of the series solution for a valid region of auxiliary parameter. Some examples were used to demonstrate the effectiveness and correctness of the proposed techniques.