poster

Heuristic computational approach using swarm intelligence in solving fractional differential equations

Authors:

Muhammad Asif Zahoor Raja,

Junaid Ali Khan,

Ijaz Mansoor QureshiAuthors Info & Claims

GECCO '10: Proceedings of the 12th annual conference companion on Genetic and evolutionary computation

Pages 2023 - 2026

https://doi.org/10.1145/1830761.1830850

Published: 07 July 2010 Publication History

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.

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Cited By

Raja MKhan JQureshi I(2018)A new stochastic approach for solution of Riccati differential equation of fractional orderAnnals of Mathematics and Artificial Intelligence10.1007/s10472-010-9222-x60:3-4(229-250)Online publication date: 28-Dec-2018
https://dl.acm.org/doi/10.1007/s10472-010-9222-x
Raja MSamar RManzar MShah S(2017)Design of unsupervised fractional neural network model optimized with interior point algorithm for solving BagleyTorvik equationMathematics and Computers in Simulation10.1016/j.matcom.2016.08.002132:C(139-158)Online publication date: 1-Feb-2017
https://dl.acm.org/doi/10.1016/j.matcom.2016.08.002
Raja MKhan JAhmad SQureshi I(2012)A new stochastic technique for painlevé equation-I using neural network optimized with swarm intelligenceComputational Intelligence and Neuroscience10.1155/2012/7218672012(4-4)Online publication date: 1-Jan-2012
https://dl.acm.org/doi/10.1155/2012/721867
Show More Cited By

Index Terms

Heuristic computational approach using swarm intelligence in solving fractional differential equations
1. Mathematics of computing
  1. Mathematical analysis
    1. Differential equations
      1. Ordinary differential equations

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cover image ACM Conferences

GECCO '10: Proceedings of the 12th annual conference companion on Genetic and evolutionary computation

July 2010

1496 pages

ISBN:9781450300735

DOI:10.1145/1830761

General Chair:
Martin Pelikan
University of Missouri, USA
,
Program Chair:
Jürgen Branke
University of Warwick, Coventry, UK

Copyright © 2010 ACM.

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SIGEVO: ACM Special Interest Group on Genetic and Evolutionary Computation

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Published: 07 July 2010

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GECCO '10: Genetic and Evolutionary Computation Conference

July 7 - 11, 2010

Oregon, Portland, USA

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Cited By

Raja MKhan JQureshi I(2018)A new stochastic approach for solution of Riccati differential equation of fractional orderAnnals of Mathematics and Artificial Intelligence10.1007/s10472-010-9222-x60:3-4(229-250)Online publication date: 28-Dec-2018
https://dl.acm.org/doi/10.1007/s10472-010-9222-x
Raja MSamar RManzar MShah S(2017)Design of unsupervised fractional neural network model optimized with interior point algorithm for solving BagleyTorvik equationMathematics and Computers in Simulation10.1016/j.matcom.2016.08.002132:C(139-158)Online publication date: 1-Feb-2017
https://dl.acm.org/doi/10.1016/j.matcom.2016.08.002
Raja MKhan JAhmad SQureshi I(2012)A new stochastic technique for painlevé equation-I using neural network optimized with swarm intelligenceComputational Intelligence and Neuroscience10.1155/2012/7218672012(4-4)Online publication date: 1-Jan-2012
https://dl.acm.org/doi/10.1155/2012/721867
Raja MKhan JQureshi I(2011)Solution of Fractional Order System of Bagley‐Torvik Equation Using Evolutionary Computational IntelligenceMathematical Problems in Engineering10.1155/2011/6750752011:1Online publication date: 22-Mar-2011
https://doi.org/10.1155/2011/675075

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