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Abstrakty
In this paper, Schauder fixed point theorem is used to prove an existence of positive continuous solutions for the nonlinear fractional order integral equation x(t) = h(t) + λ Iα (ƒ(x(t)) + g(x(t))), t ϵ [0, 1], α > 0 (E), where ƒ and g are nonlinear continuous functions and ƒ is nondecreasing while g is nonincreasing. Also the existence of maximal and minimal solutions of (E) will be proved. Some fractional order differential equations will be considered.
Słowa kluczowe
Rocznik
Tom
Strony
209-220
Opis fizyczny
Bibliogr. 16 poz.
Twórcy
autor
- Department of Mathematics, Faculty of Science, Alexandria University, Egypt, Hussdina@yahoo.com
autor
- Department of Mathematics, Faculty of Science, Alexandria University, Egypt
autor
- Department of Mathematics, Faculty of Science, Alexandria University, Egypt
Bibliografia
- [1] M. Bassam, Some existence theorems on D.E. of generalized order, J. Reine Angew. Math. (1965), 70-78.
- [2] P. J. Bushell and W. Okrasiński, Uniqueness for a class on nonlinear Volterra integral equations with convolution kernel, Math. Proc. Camb. Philos. Soc. 106 (1989), 547-552.
- [3] M. Cichoń, A. M. A. El-Sayed and A. H. Hussien, Existence theorem for nonlinear functional integral equations of fractional orders, Comment. Math. Prace Matem. 41 (2001), 59-67.
- [4] K. Deimling, Nonlinear Functional Analysis, Springer-Verlag, (1985).
- [5] A. M. A. El-Sayed. Nonlinear functional differential equations of arbitrary orders, Nonlinear Analysis TMA 33 (1998), 181-186.
- [6] A. M. A. El-Sayed, W. G. El-Sayed and O. L. Moustafa. On some fractional functional equations, Pure Mathematics and Applications, 6 (1995), 321-332. (1995).
- [7] I. M. Gelfand and G. E. Shilov, Generalized Functions, Vol. l, Moscow, (1958).
- [8] G. Gripenberg, S. O. Londen and O. Staffans, Volterra Integral and Functional Equations, Cambridge University Press, Cambridge (1990).
- [9] V. Lakshmikantham and S. Leela, Differential and Integral Inequalities, Vol. 1., Academic Press, New York, (1969).
- [10] R. H. Martin Jr., Nonlinear Operators and Differential Equations in Banach Spaces, Wiley, New York, (1976).
- [11] W. Mydlarczyk, The existence of nontrivial solutions of Volterra equations, Math. Scand. 68 (1991), 83-88.
- [12] W. Mydlarczyk, A nonlinear Able equation on the whole line, Nonlinear Analysis TMA 45 (2001), 273-279.
- [13] K. S. Miller and B. Ross, An Introduction to The Fractional Calculus and Differential Equations, John Wiley, New York, (1993).
- [14] I. Podlubny and A. M. A. El-Sayed, On two definitions of fractional calculus. Preprint UEF 03-96 (ISBN 80-7099-252-2), Slovak Academy of Science - Institute of Experimental Phys., (1996).
- [15] M. R. Rao, Ordinary Differential Equations, East-West Press, (1980).
- [16] S. Samko, A. Kilbas and I. M. Oleg, Fractional Integrals and Derivatives, Gordon and Breach Science Publisher, (1993).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.baztech-article-BUS2-0002-0057