Semigroups and some nonlinear fractional differential equations

Applied Mathematics and Computation

Volumn 149, Issue 3, 2004, Pages 823-831

  El Borai, Mahmoud M ^a  

^a Alexandria University Faculty Of Science   (Egypt)

Author keywords

Closed operators; Nonlinear fractional differential equations; Semigroups

Indexed keywords

MATHEMATICAL OPERATORS; PARTIAL DIFFERENTIAL EQUATIONS; PROBLEM SOLVING; SET THEORY; THEOREM PROVING;

CLOSED OPERATORS;

NONLINEAR EQUATIONS;

EID: 0345867025     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0096-3003(03)00188-7     Document Type: Article

References (15)

1. S.D. Zaidman, Abstract differential equations, Research Notes in Mathematics, Pitman Advanced Publishing Program, San Francisco, Londonm Melbourne, 1979.
2. M.M. El-Borai, Semigroups and incorrect problems for evolution equations, 16th IMACS WORLD CONGRESS LAUSANNE, August 2000.
3. El-Borai M.M. Some probability densities and fundamental solutions of fractional evolution equation. Chaos, Solitons & Fractals. 14:2002;433-440.
4. El-Borai M.M., Moustafa O.L., Michael F.H. On the correct for mulation of a nonlinear differential equations in Banach space. Int. J. Math. 22(1):1999.
5. El-Borai M.M. On the initial value problem for a partial differential equation with operator coefficients. Int. J. Math. Math. Sci. 3:1980.
6. M.M. El-Borai, On the correct formulation of Cauchy problem, Vectnik Moscow University, l968.
7. Gelfand I.M., Shilov G.E. Generalized Functions. vol. 1:1959;Nauka, Moscow.
8. Schneider W.R., Wayes W. Fractional diffusion and wave equation. J. Math. Phys. 30:1989.
9. Feller W. An Introduction to Probability Theory and its Application. vol. II:1971;John Wiley, New York.
10. Gorenflo R., Mainardi F. Fractional calculus and stable probability distributions. Arch. Mech. 50:1995.
11. Mainradi F. Fractional relaxation oscillation and fractional diffusion-wave phenomena. Chaos, Solitions & Fractals. 7:1996.
12. Mijatovie M., Pilipovie S., Vujzovie F. α -Timeas integrated semigroups J. Math. Anal. Appl. 210:1997.
13. Eidelman S.D. On the fundamental solution of parabolic systems. Math. Sobornik. 38:1956.
14. Pazy A. Semigroups of linear operators and applications to partial differential equations. 1983;Springer-Verlag, Berlin, New York.
15. Vladimirove V.S. Generalized Functions in Mathematical Physics. 1979;Mir, Moscow.