L¹-solutions of the boundary value problem for implicit fractional order differential equations

References

[1] S. Abbas, M. Benchohra and G. M. N’Guérékata, Topics in Fractional Differential Equations, Dev. Math. 27, Springer, New York, 2012. 10.1007/978-1-4614-4036-9Suche in Google Scholar

[2] R. P. Agarwal, M. Belmekki and M. Benchohra, A survey on semilinear differential equations and inclusions involving Riemann–Liouville fractional derivative, Adv. Difference Equ. 2009 (2009), Article ID 981728. 10.1155/2009/981728Suche in Google Scholar

[3] R. P. Agarwal, M. Benchohra and S. Hamani, A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions, Acta Appl. Math. 109 (2010), no. 3, 973–1033. 10.1007/s10440-008-9356-6Suche in Google Scholar

[4] D. Baleanu, K. Diethelm, E. Scalas and J. J. Trujillo, Fractional Calculus, Ser. Complex. Nonlinearity Chaos 3, World Scientific, Hackensack, 2012. 10.1142/8180Suche in Google Scholar

[5] M. Benchohra, J. Henderson, S. K. Ntouyas and A. Ouahab, Existence results for fractional order functional differential equations with infinite delay, J. Math. Anal. Appl. 338 (2008), no. 2, 1340–1350. 10.1016/j.jmaa.2007.06.021Suche in Google Scholar

[6] L. Byszewski, Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem, J. Math. Anal. Appl. 162 (1991), no. 2, 494–505. 10.1016/0022-247X(91)90164-USuche in Google Scholar

[7] L. Byszewski, Existence and uniqueness of mild and classical solutions of semilinear functional-differential evolution nonlocal Cauchy problem, Selected Problems of Mathematics, 50th Anniv. Cracow Univ. Technol. Anniv. Issue 6, Cracow University of Technology, Cracow (1995), 25–33. Suche in Google Scholar

[8] L. Byszewski and V. Lakshmikantham, Theorem about the existence and uniqueness of a solution of a nonlocal abstract Cauchy problem in a Banach space, Appl. Anal. 40 (1991), no. 1, 11–19. 10.1080/00036819008839989Suche in Google Scholar

[9] K. Deimling, Nonlinear Functional Analysis, Springer, Berlin, 1985. 10.1007/978-3-662-00547-7Suche in Google Scholar

[10] A. M. A. El-Sayed and S. A. Abd El-Salam, Lp-solution of weighted Cauchy-type problem of a differ-integral functional equation, Int. J. Nonlinear Sci. 5 (2008), no. 3, 281–288. Suche in Google Scholar

[11] A. M. A. El-Sayed and H. H. G. Hashem, Integrable and continuous solutions of a nonlinear quadratic integral equation, Electron. J. Qual. Theory Differ. Equ. 2008 (2008), Paper No. 25. 10.14232/ejqtde.2008.1.25Suche in Google Scholar

[12] R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, River Edge, 2000. 10.1142/3779Suche in Google Scholar

[13] A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Math. Stud. 204, Elsevier Science, Amsterdam, 2006. Suche in Google Scholar

[14] V. Lakshmikantham, S. Leela and J. Vasundhara, Theory of Fractional Dynamic Systems, Cambridge Academic, Cambridge, 2009. Suche in Google Scholar

[15] F. Mainardi, Fractional Calculus and Waves in Linear Viscoelasticity, Imperial College, London, 2010. 10.1142/p614Suche in Google Scholar

[16] M. D. Ortigueira, Fractional Calculus for Scientists and Engineers, Lect. Notes Electr. Eng. 84, Springer, Dordrecht, 2011. 10.1007/978-94-007-0747-4Suche in Google Scholar

[17] I. Podlubny, Fractional Differential Equations, Math. Sci. Eng. 198, Academic Press, San Diego, 1999. Suche in Google Scholar

[18] V. E. Tarasov, Fractional dynamics of relativistic particle, Internat. J. Theoret. Phys. 49 (2010), no. 2, 293–303. 10.1007/s10773-009-0202-zSuche in Google Scholar