Heuristic computational approach using swarm intelligence in solving fractional differential equations

Authors:
Muhammad Asif Zahoor Raja;Junaid Ali Khan;Ijaz Mansoor Qureshi
Affiliations:
International Islamic University, Islamabad, Pakistan;Interantional Islamic University, Islamabad, Pakistan;Air University, Islamabad, Pakistan
Venue:
Proceedings of the 12th annual conference companion on Genetic and evolutionary computation
Year:
2010

Citing 4
Cited 2

Neural Network Method for Solving Partial Differential Equations

Neural Processing Letters
Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies)

Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies)
Numerical algorithm for the time fractional Fokker-Planck equation

Journal of Computational Physics
Some new existence results for fractional differential inclusions with boundary conditions

Mathematical and Computer Modelling: An International Journal

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

Annals of Mathematics and Artificial Intelligence
A new stochastic technique for painlevé equation-I using neural network optimized with swarm intelligence

Computational Intelligence and Neuroscience

Quantified Score

Hi-index	0.00

Visualization

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.