A new stochastic approach for solution of Riccati differential equation of fractional order

Authors:
Muhammad Asif Raja;Junaid Ali Khan;Ijaz Mansoor Qureshi
Affiliations:
Faculty of Engineering and Technology, Department of Electronic Engineering, International Islamic University, Islamabad, Pakistan;Faculty of Engineering and Technology, Department of Electronic Engineering, International Islamic University, Islamabad, Pakistan;Department of Electronic Engineering, Air University, Islamabad, Pakistan
Venue:
Annals of Mathematics and Artificial Intelligence
Year:
2010

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Abstract

In this article, a stochastic technique has been developed for the solution of nonlinear Riccati differential equation of fractional order. Feed-forward artificial neural network is employed for accurate mathematical modeling and learning of its weights is made with heuristic computational algorithm based on swarm intelligence. In this scheme, particle swarm optimization is used as a tool for the rapid global search method, and simulating annealing for efficient local search. The scheme is equally capable of solving the integer order or fractional order Riccati differential equations. Comparison of results was made with standard approximate analytic, as well as, stochastic numerical solvers and exact solutions.