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Nonlocal Fractional Semilinear Integrodifferential Equations in Separable Banach Spaces

Received: 6 April 2014     Accepted: 15 April 2014     Published: 30 April 2014
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Abstract

The existence of mild solutions for fractional semilinear integrodifferential equations with nonlocal conditions in separable Banach spaces is studied in this article. The result is established by Hausdorff measure of noncompactness and Schauder fixed point theorem.

Published in American Journal of Applied Mathematics (Volume 2, Issue 2)
DOI 10.11648/j.ajam.20140202.13
Page(s) 60-63
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), 2014. Published by Science Publishing Group

Keywords

Fractional Differential Equation, Nonlocal Conditions, Hausdorff Measure of Noncompactness,Mild Solution

References
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[8] D. Henry, “Geometric theory of semilinear Parabolic Equations”, Lecture Notes in Math., vol.840, Springer-Verlag, New York, Berlin, 1981.
[9] A. A. Kilbas, H. M. Srivastava and J.J.Trujillo, “Theory and Applications of Fractional Differential Equations”, North Holland Mathematics Studies, vol.204, Elsevier Science B.V., Amsterdam, 2006.
[10] K. Li, J. Peng and J. Gao, “Nonlocal fractional semilinear differential equations in separable Banach spaces”, Elec. J. Diff. Eq., vol.2013, no.7, 2013, pp.1-7.
[11] Y. Lin and J. Liu, “Semilinear integrodifferential equations with nonlocal Cauchy problem”, Nonlinear Anal. vol.26 1996, pp.1023-1033.
[12] F. M. Mainardi, “Functional Calculus and Waves in Linear Viscoelasticity”, An introduction to Mathematical Models, Imperial College Press, 2010.
[13] M. M. Meerschaert, E. Nane and E. Vellaisamy, “Fractional Cauchy problems on bounded domains”, Ann. Probab.vol. 37 2009, pp.979-1007.
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[16] E. Orsingher, L. Berghin, “Time-fractional telegraph equations and telegraph processes with Brownian time”, Probab. Theory. Related Fields. Vol.128, 2004, pp.141-160.
[17] I. Podulbny, “Fractional Differential Equations”, Academic Press, New York, 1999.
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[19] X. Xue, “Semilinear nonlocal differential equations with measure of noncompactness in Banach spaces”, J. Nanjing. Univ. Math.vol.24, 2007, pp.2164-276.
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  • APA Style

    V. Dhanapalan, M. Thamilselvan, M. Chandrasekaran. (2014). Nonlocal Fractional Semilinear Integrodifferential Equations in Separable Banach Spaces. American Journal of Applied Mathematics, 2(2), 60-63. https://doi.org/10.11648/j.ajam.20140202.13

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    ACS Style

    V. Dhanapalan; M. Thamilselvan; M. Chandrasekaran. Nonlocal Fractional Semilinear Integrodifferential Equations in Separable Banach Spaces. Am. J. Appl. Math. 2014, 2(2), 60-63. doi: 10.11648/j.ajam.20140202.13

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    AMA Style

    V. Dhanapalan, M. Thamilselvan, M. Chandrasekaran. Nonlocal Fractional Semilinear Integrodifferential Equations in Separable Banach Spaces. Am J Appl Math. 2014;2(2):60-63. doi: 10.11648/j.ajam.20140202.13

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  • @article{10.11648/j.ajam.20140202.13,
      author = {V. Dhanapalan and M. Thamilselvan and M. Chandrasekaran},
      title = {Nonlocal Fractional Semilinear Integrodifferential Equations in Separable Banach Spaces},
      journal = {American Journal of Applied Mathematics},
      volume = {2},
      number = {2},
      pages = {60-63},
      doi = {10.11648/j.ajam.20140202.13},
      url = {https://doi.org/10.11648/j.ajam.20140202.13},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20140202.13},
      abstract = {The existence of mild solutions for fractional semilinear integrodifferential equations with nonlocal conditions in separable Banach spaces is studied in this article. The result is established by Hausdorff measure of noncompactness and Schauder fixed point theorem.},
     year = {2014}
    }
    

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    AU  - V. Dhanapalan
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Author Information
  • Department of Mathematics, Government College of Technology, Coimbatore-641 013, Tamilnadu, India

  • Department of Physics, Thanthai Periyar Government Institute of Technology, Vellore-632 002, Tamilnadu, India

  • Higher College of Technology, Muscat, Sultanate of Oman

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