Existence Uniqueness Theorems for Multi-Term Fractional Delay Differential Equations

References

[1] S. Abbas, Existence of solutions to fractional order ordinary and delay differential equations and applications. Electron. J. of Differ. Eq., 2011, No 9 (2011), 1-11.Search in Google Scholar

[2] R.P. Agarwal, Y. Zhou, Y. He, Existence of fractional neutral functional differential equations. Comput. Math. Appl. 59 (2010), 1095-1100.Search in Google Scholar

[3] J. Belair, M.C. Mackey, J. Mahaffy, Age-structured and two delay models for erythropoiesis. Math. Biosci. 128 (1995), 317-346.Search in Google Scholar

[4] M. Benchohra, J. Henderson, S.K. Ntouyas, A. Ouahab, Existence results for fractional order functional differential equations with infinite delay. J. Math. Anal. Appl. 338 (2008), 1340-1350.Search in Google Scholar

[5] S. Bhalekar, V. Daftardar-Gejji, D. Baleanu, R. Magin, Fractional Bloch equation with delay. Comput. Math. Appli. 61, No 5 (2011), 1355-1365.Search in Google Scholar

[6] S. Bhalekar, V. Daftardar-Gejji, Fractional ordered Liu system with time-delay. Commut. Nonlinear Sci. Numer. Simulat. 15, No 8 (2010), 2178-2191.Search in Google Scholar

[7] S. Bhalekar, V. Daftardar-Gejji, D. Baleanu, R. Magin, Generalised fractional order Bloch equation with extended delay. Int. J. Bifurcat. Chaos 22, No 4 (2012), 1250071.10.1142/S021812741250071XSearch in Google Scholar

[8] S. Choudhary, V. Daftardar-Gejji, Nonlinear multi-order fractional differential equations with periodic/ anti-periodic boundary conditions. Fract. Calc. Appl. Anal. 17, No 2 (2014), 333-347; DOI: 10.2478/s13540-014-0172-6; http://www.degruyter.com/view/j/fca.2014.17.issue-2/issue-files/fca.2014.17.issue-2.xml.10.2478/s13540-014-0172-6Search in Google Scholar

[9] L.C. Davis, Modification of the optimal velocity traffic model to include delay due to driver reaction time. Physica A 319 (2002), 557-567.Search in Google Scholar

[10] E. Fridman, L. Fridman, E. Shustin, Steady models in relay control systems with time delay and periodic disturbances. J. Dyn. Sys. Meas. Control 122 (2000), 732-737.Search in Google Scholar

[11] Y. Jalilian, R. Jalilian, Existence of solutions for delay fractional differential equations. Mediterr. J. Math. 10 (2013), 1731-1747.Search in Google Scholar

[12] M.C. Joshi, R.K. Bose, Some Topics in Non-linear Functional Analysis. Wiley Eastern Limited (1984).Search in Google Scholar

[13] L. Kexue, J. Junxiong, Existence and uniqueness of mild solutions for abstract delay fractional differential equations. Comput. Math. Appl. 62 (2011), 1398-1404.Search in Google Scholar

[14] Y. Kuang, Delay Differential Equations with Applications in Population Biology. Academic Press, Boston - New York (1993).Search in Google Scholar

[15] V. Lakshmikantham, Theory of fractional functional differential equations. Nonlinear Anal. 69 (2008), 3337-3343.Search in Google Scholar

[16] C. Liao, H. Ye, Existence of positive solutions of nonlinear fractional delay differential equations. Positivity 13 (2009), 601-609.Search in Google Scholar

[17] R. Magin, X. Feng, D. Baleanu, Solving fractional order Bloch equation. Concept. Magn. Reson. Part A 34 A (2009), 16-23.10.1002/cmr.a.20129Search in Google Scholar

[18] T.A. Maraaba, F. Jarad, D. Baleanu, On the existence and the uniqueness theorem for fractional differential equations with bounded delay within Caputo derivatives. Science in China Series A: Mathematics 51, No 10 (2008), 1775-1786.Search in Google Scholar

[19] J. Mawhin, Leray-Schauder degree: A half century of extensions and applications. Topol. Method. Nonl. An. 14 (1999), 195-228.Search in Google Scholar

[20] I. Podlubny, Fractional Differential Equations. Academic Press (1999).Search in Google Scholar

[21] H.H. Schaefer, ¨ Uber die methode der a priori-schranken. Math. Ann. 129 (1955), 415-416.Search in Google Scholar

[22] Shengli Xie, Existence results of mild solutions for impulsive fractional integro-differential evolution equations with infinite delay. Fract. Calc. Appl. Anal. 17, No 4 (2014), 1158-1174; DOI: 10.2478/s13540-014-0219-8; http://www.degruyter.com/view/j/fca.2014.17.issue-4/issue-files/fca.2014.17.issue-4.xml.10.2478/s13540-014-0219-8Search in Google Scholar

[23] Z. Yang, J. Cao, Initial value problems for arbitrary order fractional differential equations with delay. Commun. Nonlinear Sci. Numer. Simulat. 18 (2013), 2993-3005.Search in Google Scholar

[24] H. Ye, Y. Ding, J. Gao, The existence of a positive solution of Dα[x(t)x(0)] = x(t)f(t, xt). Positivity 11 (2007), 341-350.10.1007/s11117-006-2038-6Search in Google Scholar

[25] Y. Zhou, F. Jiao and J. Li, Existence, uniqueness for fractional neutral differential equations with infinite delay. Nonlinear Anal. 71 (2009), 3249-3256. Search in Google Scholar

Search in Google Scholar