Nonlocal Fractional Semilinear Integrodifferential Equations in Separable Banach Spaces

V. Dhanapalan; M. Thamilselvan; M. Chandrasekaran

doi:doi:10.11648/j.ajam.20140202.13

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Nonlocal Fractional Semilinear Integrodifferential Equations in Separable Banach Spaces

V. Dhanapalan, M. Thamilselvan, M. Chandrasekaran

Published in American Journal of Applied Mathematics (Volume 2, Issue 2)

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

[1]	J. Banas and K.Goebel, “Measure of noncompactness in Banach spaces”, Lect. Notes Pure Appl. Math., vol. 60, Marcel Dekker, New York, 1980.
[2]	E. Bazhlekova, “Fractional evolution equations in Banach spaces”, Ph.D thesis, Eindohoven University of Technology, 2001.
[3]	D. Bothe, “Multivalued perturbations of m-accretive differential inclusions”, Israel J. Math. Vol.108, 1998, pp.109-138.
[4]	L. Byszewski, “Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem”, J. Math. Anal. Appl. Vol.162, 1991, pp.494-505.
[5]	Z. Fan and G. Li, “Existence results for semilinear differential equations with nonlocal and impulsive conditions”, J.Funct. Anal. vol.258, 2010, pp.1709-1727.
[6]	X. Fu and K. Ezzinbi, “Existence of solutions of semilinear functional differential evolution equations with nonlocal conditions”, Nonlinear Anal. vol.54, 2003, pp.215-227.
[7]	M. Hahn, K. Kobayashi and S. Umarov, “Fokker–Planck- Kolmogorov equations associated with time changed fractional Brownian motion”, Proc.Amer.Math.Soc. vol.139 2011, pp. 691-705.
[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.
[14]	R.R. Nigmatullin, “To the theoretical explanation of the “universal response” ”. Phys. Stat. Sol. (b), vol. 123, 1984, pp.739-745.
[15]	S. Ntouyas and P. Tsamatos, Global existence for semilinear evolution equations with nonlocal conditions, J. Math. Anal. Appl. vol.210, 1997, pp.679-687.
[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.
[18]	S. G. Samko, A. A. Kilbas and O. I. Marichev, “Fractional Integrals and Derivatives, Theory and Applications”, Gordon and Breach, Yverdon, 1993.
[19]	X. Xue, “Semilinear nonlocal differential equations with measure of noncompactness in Banach spaces”, J. Nanjing. Univ. Math.vol.24, 2007, pp.2164-276.
[20]	X. Xue, “Existence of semilinear differential equations with nonlocal initial conditions”, Acta. Math, Sini., vol.23, 2007, pp.983-988.

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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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TY  - JOUR
T1  - Nonlocal Fractional Semilinear Integrodifferential Equations in Separable Banach Spaces
AU  - V. Dhanapalan
AU  - M. Thamilselvan
AU  - M. Chandrasekaran
Y1  - 2014/04/30
PY  - 2014
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DO  - 10.11648/j.ajam.20140202.13
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 60
EP  - 63
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20140202.13
AB  - 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.
VL  - 2
IS  - 2
ER  -

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Author Information

V. Dhanapalan

Department of Mathematics, Government College of Technology, Coimbatore-641 013, Tamilnadu, India
M. Thamilselvan

Department of Physics, Thanthai Periyar Government Institute of Technology, Vellore-632 002, Tamilnadu, India
M. Chandrasekaran

Higher College of Technology, Muscat, Sultanate of Oman

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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}
}

Copy | Download

TY  - JOUR
T1  - Nonlocal Fractional Semilinear Integrodifferential Equations in Separable Banach Spaces
AU  - V. Dhanapalan
AU  - M. Thamilselvan
AU  - M. Chandrasekaran
Y1  - 2014/04/30
PY  - 2014
N1  - https://doi.org/10.11648/j.ajam.20140202.13
DO  - 10.11648/j.ajam.20140202.13
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 60
EP  - 63
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20140202.13
AB  - 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.
VL  - 2
IS  - 2
ER  -

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