Existence results for boundary value problems of arbitrary order integrodifferential equations in Banach spaces

[1] R.P. Agarwal, M. Benchohra, S. Hamani, A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions. Acta Appl. Math. 109 (2010), 9731033.10.1007/s10440-008-9356-6Search in Google Scholar

[2] B. Ahmad, J.J. Nieto, Existence results for nonlinear boundary value problems of fractional integrodifferential equations with integral bound­ary conditions, Bound. Value Probl. 2009, Art. ID 708576, 11 pp.10.1155/2009/708576Search in Google Scholar

[3] B. Ahmad, Existence of solutions for irregular boundary value problems of nonlinear fractional differential equations, Appl. Math. Lett. 23 (2010), 390-394.10.1016/j.aml.2009.11.004Search in Google Scholar

[4] B. Ahmad, S.K. Ntouyas, A four-point nonlocal integral boundary value problem for fractional differential equations of arbitrary order, Electron. J. Qual. Theory Differ. Equ. 2011, No. 22, 15pp.10.14232/ejqtde.2011.1.22Search in Google Scholar

[5] B. Ahmad, On nonlocal boundary value problems for nonlinear integro­differential equations of arbitrary fractional order, Results in Mathemat­ics, DOI: 10.1007/s00025-011-0187-9, in press.10.1007/s00025-011-0187-9Search in Google Scholar

[6] A. Anguraj, P. Karthikeyan, and G. M. N’Guerekata, Nonlocal Cauchy problem for some fractional abstract integrodifferential equations in Ba- nach space, Commun. Appl. Anal. 55 (2009), 1-6.Search in Google Scholar

[7] D. Baleanu, O.G. Mustafa, R.P. Agarwal, An existence result for a su­perlinear fractional differential equation, Appl. Math. Lett. 23 (2010), 1129-1132.10.1016/j.aml.2010.04.049Search in Google Scholar

[8] A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, 204. Elsevier Science B.V., Amsterdam, 2006.Search in Google Scholar

[9] V. Lakshmikantham, S. Leela, J.V. Devi, Theory of Fractional Dynamic Systems, Cambridge Scientific Publishers, Cambridge (2009)Search in Google Scholar

[10] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.Search in Google Scholar

[11] J. Sabatier, O.P. Agrawal, J.A.T. Machado (Eds.), Advances in Frac­tional Calculus: Theoretical Developments and Applications in Physics and Engineering, Springer, Dordrecht, 2007.10.1007/978-1-4020-6042-7Search in Google Scholar

[12] J.R. Wang, Y. Zhou, W. Wei, H. Xu, Nonlocal problems for fractional integrodifferential equations via fractional operators and optimal controls, Comput. Math. Appl. 62 (2011), 1427-1441. 10.1016/j.camwa.2011.02.040Search in Google Scholar