| Title | EXISTENCE RESULTS FOR FRACTIONAL ORDER INTEGRAL ́ EQUATIONS OF MIXED TYPE IN FR ECHET SPACES |
| Publication Type | Journal Article |
| Year of Publication | 2009 |
| Authors | BENCHOHRA, MOUFFAK, HAMIDI, NAIMA |
| Secondary Title | Communications in Applied Analysis |
| Volume | 13 |
| Issue | 1 |
| Start Page | 111 |
| Pagination | 120 |
| Date Published | 01/2009 |
| Type of Work | scientific: mathematics |
| ISSN | 1083–2564 |
| AMS | 45D05, 47H10 |
| Abstract | In this paper we discuss the existence of solutions for an integral equation of mixed type. We rely on a generalization on Fr ́echet spaces of a Krasnosel’skii type fixed point theorem due to Avramescu and on a nonlinear alternative of Leray-Schauder type for contraction maps in Fr ́echet spaces due to Frigon and Granas. |
| URL | http://www.acadsol.eu/en/articles/13/1/11.pdf |
| Short Title | FRACTIONAL ORDER INTEGRAL EQUATIONS |
| Refereed Designation | Refereed |
| Full Text | REFERENCES[1] C. Avramescu, Some remarks on a fixed point theorem of Krasnoselskii, Electron. J. Qual. Theory Differ. Equ. 2003, No. 5, 15 pp.
[2] R.P. Agarwal, D. O’Regan and P.J.Y. Wong, Positive Solutions of Differential, Difference and Integral Equations. Kluwer Academic Publishers, Dordrecht, 1999. [3] R.P. Agarwal and D. O’Regan, Infinite Interval Problems for Differential, Difference and Integral Equations. Kluwer Academic Publishers, Dordrecht, 2001. [4] J. Banas, J. Caballero, J. Rocha and K. Sadarangani, On solutions of a quadratic integral equation of Hammerstein type, Comput. Math. Appl. 49 (5–6) (2005), 943–952.
[5] J. Banas, M. Lecko and W.G. El-Sayed, Existence theorems of some quadratic integral equations, J. Math. Anal. Appl. 222 (1998), 276–285. [6] M. Benchohra and M.A. Darwish, On monotonic solutions of a quadratic integral equation of Hammerstein type, Intern. J. Appl. Math. Sci. (to appear). [7] T.A. Burton and C. Kirk, A fixed point theorem of Kranoselskii type, Math. Nachr. 189 (1998), 23–31. [8] T.A. Burton and Bo Zhang, Fixed points and stability of an integral equation: nonuniqueness, Appl. Math. Lett. 17 (2004), 839–846. [9] G.L. Cain, Jr and M.Z. Nashed, Fixed points and stability for a sum of two operators in locally convex spaces, Pacific J. Math. 39 (3) (1971), 581–592. [10] S. Chandrasekher, Radiative Transfer, Dover Publications, New York, 1960. [11] C. Corduneanu, Integral Equations and Applications. Cambridge University Press, Cambridge, 1991. [12] K. Deimling, Nonlinear Functional Analysis, Springer-Verlag, Berlin, 1985. [13] M.A. Darwish, On quadratic integral equation of fractional orders, J. Math. Anal. Appl. 311 (2005), 112–119. [14] M. Frigon and A. Granas, Resultats de type Leray-Schauder pour des contractions sur des espaces de Fr ́echet, Ann. Sci. Math. Qu ́ebec 22 (2) (1998), 161–168. [15] S. Hu, M. Khavani and W. Zhuang, Integral equations arising in the kinetic theory of gases, Appl. Anal. 34 (1989), 261–266. [16] A.A. Kilbas, Hari M. Srivastava, and Juan J. Trujillo, Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies, 204. Elsevier Science B.V., Amsterdam, 2006. [17] C.T. Kelley, Approximation of solutions of some quadratic integral equations in transport theory, J. Integral Eq. 4 (1982), 221–237. [18] R.W. Leggett, A new approach to the H-equation of Chandrasekher, SIAM J. Math. 7 (1976), 542–550. [19] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999. [20] D. O’Regan and M. Meehan, Existence Theory for Nonlinear Integral and Integrodifferential Eguations, Kluwer Academic Publishers, Dordrecht, 1998. [21] C.A. Stuart, Existence theorems for a class of nonlinear integral equations, Math. Z. 137 (1974), 49–66. |