### Abstract

We present an efficient modern strategy for solving some well-known classes of uncertain integral equations arising in engineering and physics fields. The solution methodology is based on generating an orthogonal basis upon the obtained kernel function in the Hilbert space W 2 1 a, b in order to formulate the analytical solutions in a rapidly convergent series form in terms of their α -cut representation. The approximation solution is expressed by n -term summation of reproducing kernel functions and it is convergent to the analytical solution. Our investigations indicate that there is excellent agreement between the numerical results and the RKHS method, which is applied to some computational experiments to demonstrate the validity, performance, and superiority of the method. The present work shows the potential of the RKHS technique in solving such uncertain integral equations.

Original language | English |
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Article number | 2920463 |

Journal | Journal of Function Spaces |

Volume | 2016 |

DOIs | |

Publication status | Published - 2016 |

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### ASJC Scopus subject areas

- Analysis

### Cite this

*Journal of Function Spaces*,

*2016*, [2920463]. https://doi.org/10.1155/2016/2920463

**Solutions to Uncertain Volterra Integral Equations by Fitted Reproducing Kernel Hilbert Space Method.** / Gumah, Ghaleb; Moaddy, Khaled; Al-Smadi, Mohammed; Hashim, Ishak.

Research output: Contribution to journal › Article

*Journal of Function Spaces*, vol. 2016, 2920463. https://doi.org/10.1155/2016/2920463

}

TY - JOUR

T1 - Solutions to Uncertain Volterra Integral Equations by Fitted Reproducing Kernel Hilbert Space Method

AU - Gumah, Ghaleb

AU - Moaddy, Khaled

AU - Al-Smadi, Mohammed

AU - Hashim, Ishak

PY - 2016

Y1 - 2016

N2 - We present an efficient modern strategy for solving some well-known classes of uncertain integral equations arising in engineering and physics fields. The solution methodology is based on generating an orthogonal basis upon the obtained kernel function in the Hilbert space W 2 1 a, b in order to formulate the analytical solutions in a rapidly convergent series form in terms of their α -cut representation. The approximation solution is expressed by n -term summation of reproducing kernel functions and it is convergent to the analytical solution. Our investigations indicate that there is excellent agreement between the numerical results and the RKHS method, which is applied to some computational experiments to demonstrate the validity, performance, and superiority of the method. The present work shows the potential of the RKHS technique in solving such uncertain integral equations.

AB - We present an efficient modern strategy for solving some well-known classes of uncertain integral equations arising in engineering and physics fields. The solution methodology is based on generating an orthogonal basis upon the obtained kernel function in the Hilbert space W 2 1 a, b in order to formulate the analytical solutions in a rapidly convergent series form in terms of their α -cut representation. The approximation solution is expressed by n -term summation of reproducing kernel functions and it is convergent to the analytical solution. Our investigations indicate that there is excellent agreement between the numerical results and the RKHS method, which is applied to some computational experiments to demonstrate the validity, performance, and superiority of the method. The present work shows the potential of the RKHS technique in solving such uncertain integral equations.

UR - http://www.scopus.com/inward/record.url?scp=84979771469&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84979771469&partnerID=8YFLogxK

U2 - 10.1155/2016/2920463

DO - 10.1155/2016/2920463

M3 - Article

AN - SCOPUS:84979771469

VL - 2016

JO - Journal of Function Spaces

JF - Journal of Function Spaces

SN - 2314-8896

M1 - 2920463

ER -