Czasopismo
2012
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Vol. 52, [Z] 1
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21-28
Tytuł artykułu
Autorzy
Wybrane pełne teksty z tego czasopisma
Warianty tytułu
Języki publikacji
Abstrakty
We present an existence theorem for at least one weak solution for a coupled system of integral equations of fractional order in reflexive Banach spaces relative to the weak topology.
Czasopismo
Rocznik
Tom
Strony
21-28
Opis fizyczny
Bibliogr. 24 poz.
Twórcy
Bibliografia
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- [4] M. Cicho n , Weak solutions of ordinary differential equations in Banach spaces, Discuss. Math. Differ.Incl. Control Optim., 15 (1995), 5-14.
- [5] M. Cichoń, I. Kubiaczyk, Existence theorem for the Hammerstein integral equation, Discuss. Math. Diff. Incl., Control and Optimization, 16(2)(1996), 171-177.
- [6] Chengjun Yuan, Multiple positive solutions for (n - 1,1)-type semipositone conjugate boundary value problems for coupled systems of nonlinear fractional differential equations, Electronic Journal of Qualitative Theory of Differential Equations, 13 (2011), 1-12.
- [7] N. Dunford, j. T. Schwartz, Linear operators, Interscience, Wiley, New York, 1958.
- [8] E. Hille, R. S. Phillips, Functional Analysis and Semi-groups, Amer. Math. Soc. Colloq. Publ. 31 ,Amer. Math. Soc, Providence, R. I., 1957.
- [9] A. M. A. El-Sayed, F. M. Gaafar and H. G. H. Hashem, On the maximal and minimal solutions of arbitrary-orders nonlinear functional integral and differenbtial equations, MATH. SCi, RES.J., 8(11) (2004), 336-348.
- [10] A. M. A. El-Sayed, H. H. G. Hashem, Weak maximal and minimal solutions for Hammerstein and Urysohn integral equations in reflexive Banach spaces, Differential Equation and Control Processes. No. 4 (2008), 50-62.
- [11] V. Gafiychuk, B. Datsko, V. Meleshko, Mathematical modeling of time fractional reaction-diffusion systems, 3. Comput. Appl. Math. 220 (2008), 215-225.
- [12] V.D. Gejji, Positive solutions of a system of non-autonomous fractional differential equations, J. Math. Anal. Appl. 302 (2005), 56-64.
- [13] M.P. Lazarevic, Finite time stability analysis of PDa fractional control of robotic time-delay systems, Mech. Res. Comm. 33 (2006) 269-279.
- [14] A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations , Elsevier, North-Holland, 2006.
- [15] A. C. Me Bride, Fractional Calculus and Integral Transforms of Generalized Functions, Res. Notes in Math., vol. 31, Pitman press, San Francisco, 1974.
- [16] A. R. Mitchell, CH. Smith, An existence Theorem for weak solutions of differential equations in Banach spaces, In: Nonlinear Equations in Abstract Spaces. Proc. Int.Symp., Arlington (1977) 387-40314.
- [17] D. O'Regan, Integral equations in reflexive Banach spaces and weak topologies, Amer. Math. Soc, Vol. 124, No. 2, (1996), 607-614.
- [18] D. O'Regan, Fixed point theory for weakly sequentially continuous mapping, Math. Comput. Modeling, 27 (1998), 1-14.
- [19] H. A. H. Salem, A. M. A. El-Sayed, Fractional order integral equations in reflexive Banach spaces, Math. Slovaca., 55 , No. 2 (2005), 169-181.
- [20] B. Ross, K. S. Miller, An Introduction to Fractional Calculus and Fractional Differential Equations, John Wiley, New York (1993).
- [21] I. Podlubny, Fractional Differential equations, San Diego-NewYork-London, 1999.
- [22] S. G. Samko, A. A. Kilbas and O. Marichev, Integrals and Derivatives of Fractional Orders and Some of their Applications, Nauka i Teknika, Minsk, 1987.
- [23] X. Su, Boundary value problem for a coupled system of nonlinear fractional differential equations, Appl. Math. Lett. 22 (2009) 64-69.
- [24] V. Gafiychuk, B. Datsko, V. Meleshko, D. Blackmore, Analysis of the solutions of coupled nonlinear fractional reaction-diffusion equations, Chaos Solitons Fractals, 41 (2009) 1095-1104.
Typ dokumentu
Bibliografia
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