An operational Haar wavelet method for solving fractional Volterra integral equations

Habibollah Saeedi; Nasibeh Mollahasani; Mahmoud Mohseni Moghadam; Gennady N. Chuev

International Journal of Applied Mathematics and Computer Science (2011)

  • Volume: 21, Issue: 3, page 535-547
  • ISSN: 1641-876X

Abstract

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A Haar wavelet operational matrix is applied to fractional integration, which has not been undertaken before. The Haar wavelet approximating method is used to reduce the fractional Volterra and Abel integral equations to a system of algebraic equations. A global error bound is estimated and some numerical examples with smooth, nonsmooth, and singular solutions are considered to demonstrate the validity and applicability of the developed method.

How to cite

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Habibollah Saeedi, et al. "An operational Haar wavelet method for solving fractional Volterra integral equations." International Journal of Applied Mathematics and Computer Science 21.3 (2011): 535-547. <http://eudml.org/doc/208068>.

@article{HabibollahSaeedi2011,
abstract = {A Haar wavelet operational matrix is applied to fractional integration, which has not been undertaken before. The Haar wavelet approximating method is used to reduce the fractional Volterra and Abel integral equations to a system of algebraic equations. A global error bound is estimated and some numerical examples with smooth, nonsmooth, and singular solutions are considered to demonstrate the validity and applicability of the developed method.},
author = {Habibollah Saeedi, Nasibeh Mollahasani, Mahmoud Mohseni Moghadam, Gennady N. Chuev},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {fractional Volterra integral equation; Abel integral equation; fractional calculus; Haar wavelet method; operational matrices; error bound; numerical examples},
language = {eng},
number = {3},
pages = {535-547},
title = {An operational Haar wavelet method for solving fractional Volterra integral equations},
url = {http://eudml.org/doc/208068},
volume = {21},
year = {2011},
}

TY - JOUR
AU - Habibollah Saeedi
AU - Nasibeh Mollahasani
AU - Mahmoud Mohseni Moghadam
AU - Gennady N. Chuev
TI - An operational Haar wavelet method for solving fractional Volterra integral equations
JO - International Journal of Applied Mathematics and Computer Science
PY - 2011
VL - 21
IS - 3
SP - 535
EP - 547
AB - A Haar wavelet operational matrix is applied to fractional integration, which has not been undertaken before. The Haar wavelet approximating method is used to reduce the fractional Volterra and Abel integral equations to a system of algebraic equations. A global error bound is estimated and some numerical examples with smooth, nonsmooth, and singular solutions are considered to demonstrate the validity and applicability of the developed method.
LA - eng
KW - fractional Volterra integral equation; Abel integral equation; fractional calculus; Haar wavelet method; operational matrices; error bound; numerical examples
UR - http://eudml.org/doc/208068
ER -

References

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Citations in EuDML Documents

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  1. Babak Shiri, Sedaghat Shahmorad, Gholamreza Hojjati, Convergence analysis of piecewise continuous collocation methods for higher index integral algebraic equations of the Hessenberg type
  2. Przemysław Śliwiński, Zygmunt Hasiewicz, Paweł Wachel, A simple scheme for semi-recursive identification of Hammerstein system nonlinearity by Haar wavelets
  3. Rafał Stanisławski, Krzysztof J. Latawiec, Normalized finite fractional differences: Computational and accuracy breakthroughs

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