Title | BOUNDARY VALUE PROBLEMS FOR FRACTIONAL FUNCTIONAL DIFFERENTIAL EQUATIONS OF MIXED TYPE |
Publication Type | Journal Article |
Year of Publication | 2009 |
Authors | DARWISH, MOHAMEDABDALLA, NTOUYAS, SOTIRISK |
Secondary Title | Communications in Applied Analysis |
Volume | 13 |
Issue | 1 |
Start Page | 31 |
Pagination | 38 |
Date Published | 01/2009 |
Type of Work | scientific: mathematics |
ISSN | 1083–2564 |
AMS | 26A33, 34K05 |
Abstract | In this paper we prove some existence results for boundary value problems for a functional differential equation of fractional order with both retarded and advanced arguments. The nonlinear alternative of Leray-Schauder type is the main tool in carrying out our proof. |
URL | http://www.acadsol.eu/en/articles/13/1/4.pdf |
Short Title | FRACTIONAL FUNCTIONAL DIFFERENTIAL EQUATIONS |
Refereed Designation | Refereed |
Full Text | REFERENCES[1] O.P. Agrawal, Analytical schemes for a new class of fractional differential equations, J. Phys. A 40 (21) (2007), 5469–5477.
[2] Z. Bai and H. Lu, Positive solutions for boundary value problem of nonlinear fractional differential equation, J. Math. Anal. Appl. 311 (2005), 495–505. [3] M. A. Darwish and S. K. Ntouyas, Existence results for a fractional functional differential equation of mixed type, Commun. Appl. Nonlinear Anal. 15 (2008), 47–55. [4] V.A. Darzu-Ilea, Note on the existence of the solutions for functional differential equations of mixed type, Stud. Univ. Babe ̧s-Bolyai Math. 52(2) (2007), 51–55. [5] A.M.A. El-Sayed, Fractional-order diffusion-wave equation, Internat. J. Theoret. Phys. 35(2) (1996), 311–322. [6] A.M.A. El-Sayed and F.M. Gaafar, Fractional calculus and some intermediate physical processes, Appl. Math. Comput. 144(1) (2003), 117–126.
[7] M. El-Shahed, Positive solutions for boundary value problem of nonlinear fractional differential equation, Abstr. Appl. Anal. (2007), 1–8. [8] M. Garh, A. Rao and S.L. Kalla, Fractional generalization of temperature fields problems in oil strata, Mat. Bilten 30 (2006), 71–84. [9] R. Gorenflo, F. Mainardi, D. Moretti and P. Paradisi, Time fractional diffusion: a discrete random walk approach. Fractional order calculus and its applications, Nonlinear Dynam. 29(1-4) (2002), 129–143. [10] A. Granas and J. Dugundji, Fixed Point Theory, Springer-Verlag, New York, 2003. [11] J. Hale and S. M. Verduyn Lunel, Introduction to Functional Differential Equations, Applied Mathematical Sciences 99, Springer-Verlag, New York, 1993. [12] D. Henry, Geometric Theory of Semilinear Parabolic Partial Differential Equations, Springer-Verlag, Berlin, New York, 1989. [13] R. Hilfer, Applications of Fractional calculus in Physics, World Scientific, Singapore, 2000. [14] A.A. Kilbas and J.J. Trujillo, Differential equations of fractional order: methods, results and problems II, Appl. Anal. 81 (2002), 435–493. [15] A. A. Kilbas, H. M. Srivastava and Juan J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, 204. Elsevier Science B.V., Amsterdam, 2006. [16] V. Kolmanovskii and A. Myshkis, Introduction to the Theory and Applications of Functional-Differential Equations, Mathematics and its Applications 463, Kluwer Academic Publishers, Dordrecht, 1999. [17] V. Lakshmikantham and J.V. Devi, Theory of fractional differential equations in a Banach space, Eur. J. Pure Appl. Math. 1(1) (2008), 38–45. [18] F. Mainardi and R. Gorenflo, Time-fractional derivatives in relaxation processes: a tutorial survey, Fract. Calc. Appl. Anal. 10(3) (2007), 269–308. [19] K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Differential Equations, John Wiley, New York, 1993. [20] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999. [21] I.A. Rus and V.A. Darzu-Ilea, First order functional-differential equations with both advanced and retarded arguments, Fixed Point Theory 5(1) (2004), 103–115. [22] S.G. Samko, A.A. Kilbas and O.I. Marichev, Fractional integrals and derivatives: theory and applications, Gordon and Breach Science Publs., Amsterdam, 1993. [Russian Edition 1987] [23] R.K. Saxena and S.L. Kalla, On a fractional generalization of free electron laser equation, Appl. Math. Comput. 143 (2003), 89–97. [24] R.K. Saxena, A.M. Mathai and H.L. Haubold, On generalized fractional kinetic equations, Phys. A 344 (2004), 657–664. [25] E. Scalas, R. Gorenflo and F. Mainardi, Fractional calculus and continuous-time finance, Phys. A 284(1-4) (2000), 376–384. [26] Ch. Yu and G. Gao, Existence of fractional differential equations, J. Math. Anal. Appl. 310 (2005), 26–29. [27] S. Zhang, Positive solutions for boundary-value problems of nonlinear fractional differential equations, Electron. J. Differential Equations 36 (2006), 1–12. |