Skip to content
BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access September 25, 2015

Results for Mild solution of fractional coupled hybrid boundary value problems

  • Dumitru Baleanu , Hossein Jafari , Hasib Khan and Sarah Jane Johnston
From the journal Open Mathematics

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.

References

Search in Google Scholar

[1] Ahmad B., Ntouyas S.K., Alsaedi A.: Existence results for a system of coupled hybrid fractional differential equations, Sci. World. J., 2014, Article ID 426438, 6 pages 10.1155/2014/426438Search in Google Scholar PubMed PubMed Central

[2] Anastassiou G.A.: On right fractional calculus, Chaos, Solitons and Fractals, 2009, 42(1), 365-376 10.1016/j.chaos.2008.12.013Search in Google Scholar

[3] Atangana A.: Convergence and stability analysis of a novel iteration method for fractional Biological population equation, Neural Comput. Appl., 2014, 25(5), 1021-1030 10.1007/s00521-014-1586-0Search in Google Scholar

[4] Chai G., Hu S.: Existence of positive solutions for a fractional high-order three-point boundary value problem, Adv. Differ. Equ.-NY, 2014, 90 10.1186/1687-1847-2014-90Search in Google Scholar

[5] Herzallah M.A.E., Baleanu D.: On Fractional order hybrid differential equations, Abstr. Appl. Anal., 2014, Article ID 389386, 7 pages 10.1155/2014/389386Search in Google Scholar

[6] Hilfer (Ed.), R.: Application of fractional calculus in physics, W. Sci. Publishing Co. Singapore, 2000 10.1142/3779Search in Google Scholar

[7] Houas M., Dahmani Z.: New results for a coupled system of fractional differential equations, Facta Universitatis, Ser. Math. Inform., 2013, Vol. 28(2), 133-150 Search in Google Scholar

[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 10.22436/jmcs.014.03.05Search in Google Scholar

[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 Search in Google Scholar

[10] Kilbas A.A., Srivastava H.M., Trujillo J.J.: Theory and applications of fractional differential equations, 24, North-Holland Mathematics Studies, Amsterdam, 2006 Search in Google Scholar

[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 10.1155/2013/202650Search in Google Scholar

[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 10.1155/2014/386459Search in Google Scholar

Received: 2015-3-23
Accepted: 2015-5-15
Published Online: 2015-9-25

©2015 Dumitru Baleanu et al.

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Downloaded on 27.4.2024 from https://www.degruyter.com/document/doi/10.1515/math-2015-0055/html
Scroll to top button