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In this paper we study the existence of solution of a nonlinear integral equation of (mixed type) Volterra-Fredholm type. As an application we prove the existence of solution of an initial value problem of fractional order in the space of Lebesgue integrable functions on the interval [0,1].
Wydawca
Rocznik
Tom
Strony
237--247
Opis fizyczny
Bibliogr. 14 poz.
Twórcy
autor
- Faculty of Science, Alexandria University, Egypt
autor
- Faculty of Science, Alexandria University, Egypt
autor
- Faculty of Science, Alexandria University, Egypt
Bibliografia
- [1] J. Banaś, On the supperposition operator and integrable solutions of some functional equation, Nonlinear Analysis T.M.A., 12 (1988), 777-784.
- [2] J. Banaś, Applications of measures of weak noncompactness and some classes of operators in the theory of functional equations in the Lebesgue space, Nonlinear Analysis T.M.A. 30(6) (1997), 3283-3293.
- [3] A. M. A. El-Sayed, Nonlinear functional differential equations of arbitrary orders, Nonlinear Analysis, T.M.A. 33(2) (1998), 181-186.
- [4] A. M. A. El-Sayed, W. G. El-Sayed and O. L. Moustafa, On some fractional functional equations, PU.M.A 6(4) (1995), 321-332.
- [5] A. M. A. El-Sayed, N. Sherif and I. A. Ibrahim, On an operator functional equation in \(L^1 [0, \infty)\) and Volterra-Fredholm type integral equations, Comment. Math. Prace Matem. 43(1) (2003), 63-76.
- [6] W. G. El-Sayed, and A. M. A. El-Sayed, On the functional integral equations of mixed type and integro-differential equations of fractional orders, Appl. Math. and Comput., to appear.
- [7] G. Emmanuele, Integrable solutions of a functional-integral equation, J. Integral Equations Appl.Rev. 4(1) (1992), 89-94.
- [8] K. Goebel and W. A. Kirk, Topics in Metric Fixed Point Theory, Cambridge University Press 1990.
- [9] M. A. Krasnoselskii, On the continuity of the operator F u(x) = f (x, u(x)), Dokl.Akad. Nauk SSSR 77 (1951), 185-188 (in Russian).
- [10] M. A. Krasnoselskii, P. P. Zabrejko, J. I. Pustylnik and P. J. Sobolevskii, Integral Operators in Spaces of Summable Functions, Nauka Moscow 1966, (English Translation: Noordhoff Leyden 1976).
- [11] K. S. Miller and B. Ross, An Introduction to Fractional Calculus and Fractional Differential Equations, John Wiley and Sons New York 1993.
- [12] I. Podlubny and A. M. A. El-Sayed, On two definitions of fractional derivative, PreprintUEF-03-96, Slovak Academy of Sciences, Institute of Experimental Physics 1996.
- [13] G. Scorza Dragoni, Un teorema sulle funzioni continue rispetto ad une e misurabili rispetto ad un’altra variable, Rend. Sem. Mat. Univ. Padova 17 1948, 102-106.
- [14] P. P. Zabrejko, A. I. Koshelev, M. A. Krasnoselskii, S. G. Mikhlin, L. S. Rakovshchik and V. J. Stecenko, Integral equations, Noordhoff Leyden 1975.
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Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUS2-0008-0059