Existence and Uniqueness of Mild Solutions for Fractional Integrodifferential Equations

V. Dhanapalan; M. Thamilselvan; M. Chandrasekaran

doi:doi:10.11648/j.acm.20140301.15

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Existence and Uniqueness of Mild Solutions for Fractional Integrodifferential Equations

V. Dhanapalan, M. Thamilselvan, M. Chandrasekaran

Published in Applied and Computational Mathematics (Volume 3, Issue 1)

Received: 30 January 2014 Published: 10 March 2014

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Abstract

The aim of this paper is to prove the existence and uniqueness of mild solution of a class of l nonlinear fractional integrodifferential equations {█((d^q u(t))/(dt^q )+Au(t)=∫_0^t▒f(t,s,x(s) )ds+∫_0^t▒〖a(t-s)g(s,y(s) )ds, t∈[0,T],〗@u(0)=u_(o.) )┤ in a Banach space X, where 0

Published in	Applied and Computational Mathematics (Volume 3, Issue 1)
DOI	10.11648/j.acm.20140301.15
Page(s)	32-37
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

Integrodifferential Equation, Fractional Equation, Mild Solution, Compact Semigroup, Krasnoselskii Theorem, Semi Group of Linear Operators

References

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APA Style

V. Dhanapalan, M. Thamilselvan, M. Chandrasekaran. (2014). Existence and Uniqueness of Mild Solutions for Fractional Integrodifferential Equations. Applied and Computational Mathematics, 3(1), 32-37. https://doi.org/10.11648/j.acm.20140301.15

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ACS Style

V. Dhanapalan; M. Thamilselvan; M. Chandrasekaran. Existence and Uniqueness of Mild Solutions for Fractional Integrodifferential Equations. Appl. Comput. Math. 2014, 3(1), 32-37. doi: 10.11648/j.acm.20140301.15

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AMA Style

V. Dhanapalan, M. Thamilselvan, M. Chandrasekaran. Existence and Uniqueness of Mild Solutions for Fractional Integrodifferential Equations. Appl Comput Math. 2014;3(1):32-37. doi: 10.11648/j.acm.20140301.15

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@article{10.11648/j.acm.20140301.15,
  author = {V. Dhanapalan and M. Thamilselvan and M. Chandrasekaran},
  title = {Existence and Uniqueness of Mild Solutions for Fractional Integrodifferential Equations},
  journal = {Applied and Computational Mathematics},
  volume = {3},
  number = {1},
  pages = {32-37},
  doi = {10.11648/j.acm.20140301.15},
  url = {https://doi.org/10.11648/j.acm.20140301.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20140301.15},
  abstract = {The aim of this paper is to prove the existence and uniqueness of mild solution of a class of l nonlinear fractional integrodifferential equations {█((d^q u(t))/(dt^q )+Au(t)=∫_0^t▒f(t,s,x(s) )ds+∫_0^t▒〖a(t-s)g(s,y(s) )ds,    t∈[0,T],〗@u(0)=u_(o.) )┤ in a Banach space X, where 0
											
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TY  - JOUR
T1  - Existence and Uniqueness of Mild Solutions for Fractional Integrodifferential Equations
AU  - V. Dhanapalan
AU  - M. Thamilselvan
AU  - M. Chandrasekaran
Y1  - 2014/03/10
PY  - 2014
N1  - https://doi.org/10.11648/j.acm.20140301.15
DO  - 10.11648/j.acm.20140301.15
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
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EP  - 37
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20140301.15
AB  - The aim of this paper is to prove the existence and uniqueness of mild solution of a class of l nonlinear fractional integrodifferential equations {█((d^q u(t))/(dt^q )+Au(t)=∫_0^t▒f(t,s,x(s) )ds+∫_0^t▒〖a(t-s)g(s,y(s) )ds,    t∈[0,T],〗@u(0)=u_(o.) )┤ in a Banach space X, where 0
											
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Author Information

V. Dhanapalan

Government College of Technology, Coimbatore-641013.Tamilnadu, India
M. Thamilselvan

Thanthai Periyar Government Institute of Technology, Vellore-632002.Tamilnadu, India
M. Chandrasekaran

Higher College of Technology, Muscat, the Sultanate of Oman

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APA Style

V. Dhanapalan, M. Thamilselvan, M. Chandrasekaran. (2014). Existence and Uniqueness of Mild Solutions for Fractional Integrodifferential Equations. Applied and Computational Mathematics, 3(1), 32-37. https://doi.org/10.11648/j.acm.20140301.15

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ACS Style

V. Dhanapalan; M. Thamilselvan; M. Chandrasekaran. Existence and Uniqueness of Mild Solutions for Fractional Integrodifferential Equations. Appl. Comput. Math. 2014, 3(1), 32-37. doi: 10.11648/j.acm.20140301.15

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AMA Style

V. Dhanapalan, M. Thamilselvan, M. Chandrasekaran. Existence and Uniqueness of Mild Solutions for Fractional Integrodifferential Equations. Appl Comput Math. 2014;3(1):32-37. doi: 10.11648/j.acm.20140301.15

Copy | Download

@article{10.11648/j.acm.20140301.15,
  author = {V. Dhanapalan and M. Thamilselvan and M. Chandrasekaran},
  title = {Existence and Uniqueness of Mild Solutions for Fractional Integrodifferential Equations},
  journal = {Applied and Computational Mathematics},
  volume = {3},
  number = {1},
  pages = {32-37},
  doi = {10.11648/j.acm.20140301.15},
  url = {https://doi.org/10.11648/j.acm.20140301.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20140301.15},
  abstract = {The aim of this paper is to prove the existence and uniqueness of mild solution of a class of l nonlinear fractional integrodifferential equations {█((d^q u(t))/(dt^q )+Au(t)=∫_0^t▒f(t,s,x(s) )ds+∫_0^t▒〖a(t-s)g(s,y(s) )ds,    t∈[0,T],〗@u(0)=u_(o.) )┤ in a Banach space X, where 0
									
										Copy
										|
										Download

TY  - JOUR
T1  - Existence and Uniqueness of Mild Solutions for Fractional Integrodifferential Equations
AU  - V. Dhanapalan
AU  - M. Thamilselvan
AU  - M. Chandrasekaran
Y1  - 2014/03/10
PY  - 2014
N1  - https://doi.org/10.11648/j.acm.20140301.15
DO  - 10.11648/j.acm.20140301.15
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 32
EP  - 37
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20140301.15
AB  - The aim of this paper is to prove the existence and uniqueness of mild solution of a class of l nonlinear fractional integrodifferential equations {█((d^q u(t))/(dt^q )+Au(t)=∫_0^t▒f(t,s,x(s) )ds+∫_0^t▒〖a(t-s)g(s,y(s) )ds,    t∈[0,T],〗@u(0)=u_(o.) )┤ in a Banach space X, where 0
									
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