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

Adil Mısır

doi:doi:10.11648/j.dmath.20160101.14

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

Adil Mısır

Published in International Journal of Discrete Mathematics (Volume 1, Issue 1)

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.

Published in	International Journal of Discrete Mathematics (Volume 1, Issue 1)
DOI	10.11648/j.dmath.20160101.14
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), 2017. 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.
[15]	D. B. Pachpatte, On approximate solutions of a Volterra type integrodifferential equation on time scales, Int. Journal of Math. Analysis, 4 (34) (2010) 1651-1659.
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[18]	A. M. Wazwaz, The combined Laplace transforms-Adomain decomposition method for handling nonlinear Voltera integro-diferential equations, Appl. Math. Comput. 216 (2010) 1304-1309.
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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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ACS 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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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://article.sciencepublishinggroup.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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TY  - JOUR
T1  - An Analytic Approach to Weakly-Singular Integro-Dynamic Equation on Time Scales
AU  - Adil Mısır
Y1  - 2017/01/16
PY  - 2017
N1  - https://doi.org/10.11648/j.dmath.20160101.14
DO  - 10.11648/j.dmath.20160101.14
T2  - International Journal of Discrete Mathematics
JF  - International Journal of Discrete Mathematics
JO  - International Journal of Discrete Mathematics
SP  - 20
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PB  - Science Publishing Group
SN  - 2578-9252
UR  - https://doi.org/10.11648/j.dmath.20160101.14
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.
VL  - 1
IS  - 1
ER  -

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Adil Mısır

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APA Style

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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ACS 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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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://article.sciencepublishinggroup.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}
}

Copy | Download

TY  - JOUR
T1  - An Analytic Approach to Weakly-Singular Integro-Dynamic Equation on Time Scales
AU  - Adil Mısır
Y1  - 2017/01/16
PY  - 2017
N1  - https://doi.org/10.11648/j.dmath.20160101.14
DO  - 10.11648/j.dmath.20160101.14
T2  - International Journal of Discrete Mathematics
JF  - International Journal of Discrete Mathematics
JO  - International Journal of Discrete Mathematics
SP  - 20
EP  - 29
PB  - Science Publishing Group
SN  - 2578-9252
UR  - https://doi.org/10.11648/j.dmath.20160101.14
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.
VL  - 1
IS  - 1
ER  -

Copy | Download