Existence and uniqueness results of some fractional boundary value problem

• Autorzy: Seddiki H. , Mazouzi S.
• Języki publikacji: EN

Abstrakty

EN

We establish in this paper some existence results of a solution to a boundary value problem of fractional differential equation. We obtain two results, the first one by the Banach fixed point theorem and the second by a nonlinear alternative of Leray-Schauder type.

Słowa kluczowe

EN

boundary value problem; fractional differential equation; fixed point theorem

PL

zagadnienie brzegowe; ułamkowe równanie różniczkowe; twierdzenie o punkcie stałym

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2011
• Tom: Vol. 17, nr 1
• Strony: 91--103
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Seddiki H.

autor

Mazouzi S.

• Departement Des Sciences Fondamentales, University 20 Aout 1955, BP 26, Skikda 21000, Algeria,

Bibliografia

• [1] R. L. Bagley and R. A. Calico, Fractional order state equations for the control of viscoelastic structures, J. Guidance Control Dynam. 14 (1991), 304-311.
• [2] M. Benchohra, S. Hamani and S. K. Ntouyas, Boundary value problems for differential equation with fractional order, Surv. Math. Appl. 3 (2008), 1-12.
• [3] D. A. Benson, S. W. Wheateraft and M. M. Meerschaert, Application of fractional advection-dispersion equation, Water Resour. Res. 36 (2000), no. 6, 1403-1412.
• [4] D. Delbosco and L. Rodino, Existence and uniqueness for a nonlinear fractional differential equation, J. Math. Anal. Appl. 204 (1996), 609-625.
• [5] J. Dungundi and A. Granas, Fixed Point Theory, Springer Monographs in Mathematics, Springer-Verlag, New York, 2003.
• [6] A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies 204, Elsevier, Amsterdam, 2006.
• [7] R. C. Koeller, Application of fractional calculus to the theory of viscoelasticity, J. Appl. Mech. 51 (1984), 299-307.
• [8] Y. Luchko, Some uniqueness and existence results for the initial boundary value problems for the generalized time-fractional diffusion equation, Comput. Math. Appl. 59(2010), 1766-1772.
• [9] R. J. Mark and M. W. Hall, Differintegral interpolation from a band limited signal's samples, IEEE Trans. Acoust. Speech Signal Process. 29 (1981), 872-877.
• [10] M. Rudda and C. C. Tisdell, On the solvability of two-point, second-order boundary value problems, Appl. Math. Lett. 20 (2007), 824-828.
• [11] H. H. Sun, A. A. Abdelwahab and B. Onarel, Linear approximation of transfer function with a pole of fractional order, IEEE Trans. Automat. Control 29 (1984), 441-444.