Heuristic computational approach using swarm intelligence in solving fractional differential equations

Abstract

In this paper, a heuristic computational intelligence approach has been presented for solving the differential equations of fractional order. The strength of feed forward artificial neural networks is used to mathematically model the equations and particle swarm optimization algorithm is applied for learning of weights, aided by simulating annealing algorithm for rapid local search. The design scheme has been successfully applied to solve different types of linear ordinary differential equations of fractional order. The results were compared with exact solutions, analytic solution and standard numerical techniques. In case of simple linear ordinary fractional differential equations, relatively more precise solutions were obtained than standard numerical methods. However, for complex linear fractional differential equation, the same scheme is applicable, but with reduced accuracy. The advantage of this approach is that the solution is available on the domain of continuous inputs unlike the other numerical techniques.