Positive integrable solutions for nonlinear integral and differential inclusions of fractional-orders

• Autorzy: Al-Issa S. , El-Sayed A.M.A.
• Języki publikacji: EN

Abstrakty

EN

In this paper we study the global existence of positive integrable solution for the nonlinear integral inclusion of fractional order..[formula] As an application the global existence of the solution for the initial-value problem of the arbitrary (fractional) orders differential inclusion..[formula] will be studied.

Słowa kluczowe

EN

integral inclusion; fractional calculus; Caratheodory condition; differential inclusion; fixed point theorem

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2009
• Tom: Vol. 49, [Z] 2
• Strony: 171--177
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Al-Issa S.

autor

El-Sayed A.M.A.

• Faculty of Science, Beirut Arab University Beirut, Lebanon,

Bibliografia

• [1] A. Bressan and G. Colombo, Extensions and selections of maps with decomposable values, Studia Math. 90 (1988), 69-86.
• [2] M. Caputom, Linear model of dissipation whose Q is almost frequency independent II, Geophys. J. R. Astr. Soc. Vol. 13 (1967), 529-539.
• [3] M. Cichoń, Multivalued perturbations of m-accretive differential inclusions in a non-separable Banach space, Commentationes Math. 32 (1992), 11-17.
• [4] K. Deimling, Nonlinear Functional Analysis, Springer-Verlag, 1985.
• [5] J. Dungundji and A. Granas, Fixed Piont Theory, Monografie Mathematyczne, PWN, Warsaw, 1982.
• [6] M. Cichoń, A. M. A. El-Sayed and A.H. Hussien, Existence theorems for nonlinear functional integral equations of fractional orders, Comm. Math. Prace Matem. 41 (2001), 5-67.
• [7] K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley and Sons Inc., 1993.
• [8] I. Podlubny and A. M. A. EL-Sayed, On two defintions of fractional calculus, Preprint UEF 03-69 (ISBN 80-7099-252-2), Solvak Academy of Science-Institute of Experimental Phys., 1996.
• [9] I. Podlubny. Fractional Differential Equation, Acad. Press, San Diego-New York-London, 1999.
• [10] D. Repovs, P.V. Semenov, Continuous Selection of Multivalued Mappings, Kluwer Academic Press, 1988.
• [11] S. G. Samko, A. A. Kilbas, O. Marichev, Integrals and Derivatives of Fractional Orders and Some of their Applications, Nauka i Teknika, Minsk, 1987.
• [12] C. Swartz, Measure, Integration and Function Spaces, World Scientific, Singapore, 1994.