Article ID Journal Published Year Pages File Type
1703197 Applied Mathematical Modelling 2015 19 Pages PDF
Abstract
A new computational intelligence technique is presented for solution of non-linear quadratic Riccati differential equations of fractional order based on artificial neural networks (ANNs) and sequential quadratic programming (SQP). The power of feed forward ANNs in an unsupervised manner is exploited for mathematical modeling of the equation; training of weights is carried out with an efficient constrained optimization technique based on the SQP algorithm. The proposed scheme is evaluated on two initial value problems of the Riccati fractional order equation with integer and non-integer derivatives. Comparison of results with the exact solution, and with reference numerical methods demonstrates the correctness of the proposed methodology. Performance of the proposed scheme is also validated using results of statistical analysis based on a sufficiently large number of independent runs.
Related Topics
Physical Sciences and Engineering Engineering Computational Mechanics
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