A coupled system of fractional order integral equations in reflexive Banach spaces

• Autorzy: El-Sayed A.M.A. , Hashem H.H.G.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

weak solutions; Pettis-integral of fractional order integration; coupled system

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2012
• Tom: Vol. 52, [Z] 1
• Strony: 21--28
• Opis fizyczny: Bibliogr. 24 poz.

Twórcy

autor

El-Sayed A.M.A.

autor

Hashem H.H.G.

• Faculty of Science, Alexandria University Alexandria, Egypt,

Bibliografia

• [1] Bashir Ahmad, Juan J. Nieto, Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions, Computers and Mathematics with Applications, 58 (2009) 1838-1843.
• [2] C. Bai, J. Fang, The existence of a positive solution for a singular coupled system of nonlinear fractional differential equations, Appl. Math. Comput. 150 (2004) 611-621.
• [3] Y. Chen, H. An, Numerical solutions of coupled Burgers equations with time and space fractional derivatives, Appl. Math. Comput. 200 (2008) 87-95.
• [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.