Results for Mild solution of fractional coupled hybrid boundary value problems

Dumitru Baleanu; Hossein Jafari; Hasib Khan; Sarah Jane Johnston

Open Mathematics (2015)

  • Volume: 13, Issue: 1
  • ISSN: 2391-5455

Abstract

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The study of coupled system of hybrid fractional differential equations (HFDEs) needs the attention of scientists for the exploration of its different important aspects. Our aim in this paper is to study the existence and uniqueness of mild solution (EUMS) of a coupled system of HFDEs. The novelty of this work is the study of a coupled system of fractional order hybrid boundary value problems (HBVP) with n initial and boundary hybrid conditions. For this purpose, we are utilizing some classical results, Leray–Schauder Alternative (LSA) and Banach Contraction Principle (BCP). Some examples are given for the illustration of applications of our results.

How to cite

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Dumitru Baleanu, et al. "Results for Mild solution of fractional coupled hybrid boundary value problems." Open Mathematics 13.1 (2015): null. <http://eudml.org/doc/275976>.

@article{DumitruBaleanu2015,
abstract = {The study of coupled system of hybrid fractional differential equations (HFDEs) needs the attention of scientists for the exploration of its different important aspects. Our aim in this paper is to study the existence and uniqueness of mild solution (EUMS) of a coupled system of HFDEs. The novelty of this work is the study of a coupled system of fractional order hybrid boundary value problems (HBVP) with n initial and boundary hybrid conditions. For this purpose, we are utilizing some classical results, Leray–Schauder Alternative (LSA) and Banach Contraction Principle (BCP). Some examples are given for the illustration of applications of our results.},
author = {Dumitru Baleanu, Hossein Jafari, Hasib Khan, Sarah Jane Johnston},
journal = {Open Mathematics},
keywords = {Hybrid fractional differential equations; Existence and uniqueness of Mild solution; Leray–Schauder Alternative; Banach Contraction Principle},
language = {eng},
number = {1},
pages = {null},
title = {Results for Mild solution of fractional coupled hybrid boundary value problems},
url = {http://eudml.org/doc/275976},
volume = {13},
year = {2015},
}

TY - JOUR
AU - Dumitru Baleanu
AU - Hossein Jafari
AU - Hasib Khan
AU - Sarah Jane Johnston
TI - Results for Mild solution of fractional coupled hybrid boundary value problems
JO - Open Mathematics
PY - 2015
VL - 13
IS - 1
SP - null
AB - The study of coupled system of hybrid fractional differential equations (HFDEs) needs the attention of scientists for the exploration of its different important aspects. Our aim in this paper is to study the existence and uniqueness of mild solution (EUMS) of a coupled system of HFDEs. The novelty of this work is the study of a coupled system of fractional order hybrid boundary value problems (HBVP) with n initial and boundary hybrid conditions. For this purpose, we are utilizing some classical results, Leray–Schauder Alternative (LSA) and Banach Contraction Principle (BCP). Some examples are given for the illustration of applications of our results.
LA - eng
KW - Hybrid fractional differential equations; Existence and uniqueness of Mild solution; Leray–Schauder Alternative; Banach Contraction Principle
UR - http://eudml.org/doc/275976
ER -

References

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  9. [8] Khan H., Alipour M., Khan R.A., Tajadodi H., Khan A.: On approximate solution of fractional order Logistic equations by operational matrices of Bernstein polynomials, J. Math. Comp. Sci., 2014, 14 (2015), 222-232 
  10. [9] Khan R.A., Khan A., Samad A., Khan H.: On existence of solutions for fractional differential equations with P-Laplacian operator, J. Fract. Calc. Appl., 2014, Vol. 5(2) July, pp. 28-37 
  11. [10] Kilbas A.A., Srivastava H.M., Trujillo J.J.: Theory and applications of fractional differential equations, 24, North-Holland Mathematics Studies, Amsterdam, 2006 Zbl1092.45003
  12. [11] Yang Y.J., Baleanu D., Yang X.J.: A Local fractional variational iteration method for Laplace equation with in local fractional operators, Abstr. Appl. Anal., 2013, Article ID 202650, 6 pages Zbl1273.65158
  13. [12] Zhao C.G., Yang A.M., Jafari H., Haghbin A.: The Yang-Laplace transform for solving the IVPs with local fractional derivative, Abstr. Appl. Anal., 2014, Article ID 386459, 5 pages 

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