Neural Network Method for Solving Partial Differential Equations
Neural Processing Letters
Solving differential equations with genetic programming
Genetic Programming and Evolvable Machines
Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies)
Introduction to Genetic Algorithms
Introduction to Genetic Algorithms
On the fractional Adams method
Computers & Mathematics with Applications
A new stochastic approach for solution of Riccati differential equation of fractional order
Annals of Mathematics and Artificial Intelligence
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In this paper, a stochastic computational intelligence approach for solution of fractional differential equations has been used. In this method, the strength of feed forward artificial neural networks is used to accurately model the equation and Genetic algorithm applied for learning of weights aided by active set algorithm for rapid local search. The design scheme has been successfully applied to solve different types of linear and nonlinear ordinary fractional differential equations. The results were compared with exact solutions, approximate analytic solution and standard numerical techniques. In case of linear ordinary fractional differential equations, relatively more accurate solutions were obtained than standard numerical methods. However, for complex nonlinear fractional differential equation, the same scheme is applicable, but with reduced accuracy. The advantage of this approach is that it provides the solution on continuous entire finite domain unlike the other numerical techniques.