International Journal of Discrete Mathematics

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An Analytic Approach to Weakly-Singular Integro-Dynamic Equation on Time Scales

Received: 12 December 2016    Accepted: 22 December 2016    Published: 16 January 2017
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Abstract

In this paper, we present a new and simple approach to resolve linear and nonlinear weakly-singular Volterra integro-dynamic equations of first and second order on any time scales. In order to eliminate the singularity of the equation, nabla derivative is used and then transforming the given first-order integro-dynamic equations onto an first-order dynamic equations on time scales. The validity of the method is illustrated with some examples.

DOI 10.11648/j.dmath.20160101.14
Published in International Journal of Discrete Mathematics (Volume 1, Issue 1, December 2016)
Page(s) 20-29
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Time Scales, Integro-Dynamic Equations, Volterra Integro-Differential Equation

References
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[14] A. Mısır, S. Öğrekçi, On approximate solution of first-order weakly-singular Volterra integro-dynamic equation on time scales, Gazi University Journal of Science, 28 (4) (2015) 651–658.
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    Adil Mısır. (2017). An Analytic Approach to Weakly-Singular Integro-Dynamic Equation on Time Scales. International Journal of Discrete Mathematics, 1(1), 20-29. https://doi.org/10.11648/j.dmath.20160101.14

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    Adil Mısır. An Analytic Approach to Weakly-Singular Integro-Dynamic Equation on Time Scales. Int. J. Discrete Math. 2017, 1(1), 20-29. doi: 10.11648/j.dmath.20160101.14

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    AMA Style

    Adil Mısır. An Analytic Approach to Weakly-Singular Integro-Dynamic Equation on Time Scales. Int J Discrete Math. 2017;1(1):20-29. doi: 10.11648/j.dmath.20160101.14

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  • @article{10.11648/j.dmath.20160101.14,
      author = {Adil Mısır},
      title = {An Analytic Approach to Weakly-Singular Integro-Dynamic Equation on Time Scales},
      journal = {International Journal of Discrete Mathematics},
      volume = {1},
      number = {1},
      pages = {20-29},
      doi = {10.11648/j.dmath.20160101.14},
      url = {https://doi.org/10.11648/j.dmath.20160101.14},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.dmath.20160101.14},
      abstract = {In this paper, we present a new and simple approach to resolve linear and nonlinear weakly-singular Volterra integro-dynamic equations of first and second order on any time scales. In order to eliminate the singularity of the equation, nabla derivative is used and then transforming the given first-order integro-dynamic equations onto an first-order dynamic equations on time scales. The validity of the method is illustrated with some examples.},
     year = {2017}
    }
    

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    AB  - In this paper, we present a new and simple approach to resolve linear and nonlinear weakly-singular Volterra integro-dynamic equations of first and second order on any time scales. In order to eliminate the singularity of the equation, nabla derivative is used and then transforming the given first-order integro-dynamic equations onto an first-order dynamic equations on time scales. The validity of the method is illustrated with some examples.
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