Geodesic
Weak solution for fractional order integral equations in reflexive Banach spaces
Mathematica slovaca, Tome 55 (2005) no. 2, pp. 169-181
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Classification : 26A33, 34A12, 47G10 
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Salem, Hussein A. H.; El-Sayed, Ahmed M. A. Weak solution for fractional order integral equations in reflexive Banach spaces. Mathematica slovaca, Tome 55 (2005) no. 2, pp. 169-181. http://geodesic.mathdoc.fr/item/MASLO_2005_55_2_a3/

[1] AL-ABEDEEN A. Z.-ARORA H. L.: A global existence and uniqueness theorem for ordinary differential equations of generalized order. Canad. Math. Bull. 21 (1978), 267-271. | MR | Zbl

[2] ARINO O.-GAUTIER S.-PENOT T. P. : A fixed point theorem for sequentially continuous mappings with application to ordinary differential equations. Funkcial. Ekvac 27 (1984), 273-279. | MR | Zbl

[3] BASSAM M.: Some existence theorems on differential equations of generalized order. J. Reine Angew. Math. 218 (1965), 70-78. | MR | Zbl

[4] CICHOŃ M.: Weak solutions of ordinary differential equations in Banach spaces. Discuss. Math. Differ. Inch Control Optim. 15 (1995), 5-14. | MR

[5] CICHOŃ M.-EL-SAYED A. M.-SALEM H. A. H.: Existence theorem for nonlinear functional integral equations of fractional orders. Comment. Math. Prace Mat. 41 (2001), 59-67. | MR

[6] CRAMER E.-LAKSHMIKANTHAM V.-MITCHELL A. R.: On the existence of weak solutions of differential equations in nonreflexive Banach spaces. Nonlinear Anal. 2 (1978), 259-262. | MR | Zbl

[7] DIESTEL J.-UHL J. J., Jr.: Vector Measures. Math. Surveys Monogr. 15, Amer. Math. Soc, Providence, R.I., 1977. | MR | Zbl

[8] EDGAR G. A.: Geometry and the Pettis-integral. Indiana Univ. Math. J. 26 (1977), 663-677.

[9] EDGAR G. A.: Geometry and the Pettis-integral II. Indiana Univ. Math. J. 28 (1979), 559-579.

[10] EL-SAYED A. M.-EL-SAYED W. G.-MOUSTAFA O. L.: On some fractional functional equations. Pure. Math. Appl. 6 (1995), 321-332. | MR | Zbl

[11] EL-SAYED A. M. A.: Nonlinear functional differential equations of arbitrary orders. Nonlinear Anal. 33 (1998), 181-186. | MR | Zbl

[12] EL-SAYED A. M. A.-IBRAHIM A. G.: Set-valued integral equations of arbitrary (fractional) order. Appl. Math. Comput. 118 (2001), 113-121. | MR

[13] GEITZ R. F.: Pettis integration. Proc Amer. Math. Soc 82 (1981), 81-86. | MR | Zbl

[14] GEITZ R. F.: Geometry and the Pettis integration. Trans. Amer. Math. Soc. 269 (1982), 535-548. | MR

[15] HADID S. B. : Local and global existence theorem on differential equation on non integral order. Math. Z. 7 (1995), 101-105. | MR

[16] HILLE E.-PHILLIPS R. S.: Functional Analysis and Semi-groups. Amer. Math. Soc. Colloq. Publ. 31, Amer. Math. Soc, Providence, R.I., 1957. | MR

[17] KNIGHT W. J.: Solutions of differential equations in B-spaces. Duke Math. J. 41 (1974), 437-442. | MR | Zbl

[18] KUBIACZYK I.-SZUFLA S.: Kneser's theorem for weak solutions of ordinary differential equations in Banach spaces. Publ. Inst. Math. (Beograd) (N.S.) 32(46) (1982), 99-103. | MR | Zbl

[19] MILLER K. S.-ROSS B.: An Introduction to the Fractional Calculus and Fractional Differential Equations. John Wiley, New York, 1993. | MR | Zbl

[20] MITCHELL A. R.-SMITH, CH.: An existence theorem for weak solutions of differential equations in Banach spaces. In: Nonlinear Equations in Abstract Spaces. Proc. Int. Symp., Arlington 1977, 1978, pp. 387-403. | MR

[21] O'REGAN D.: Fixed point theory for weakly sequentially continuous mapping. Math. Comput. Modeling 27 (1998), 1-14.

[22] PETTIS B. J.: On integration in vector spaces. Trans. Amer. Math. Soc. 44 (1938), 277-304. | MR | Zbl

[23] PHILLIPS R. S.: Integration in a convex linear topological space. Trans. Amer. Math. Soc. 47 (1940), 114-115. | MR | Zbl

[24] PODLUBNY I.-EL-SAYED A. M. A.: On two definitions of fractional calculus. In: Preprint UEF-03-96, Slovak Academy of Sciences, Institute of Experimental Phys., 1996.

[25] PODLUBNY I.: Fractional Differential Equation. Acad. Press, San Diego-New York-London, 1999.

[26] SALEM H. A. H.-EL-SAYED A. M. A.-MOUSTAFA O. L.: Continuous solutions of some nonlinear fractional order integral equations. Comment. Math. Prace Mat. 42 (2002), 209-220. | MR

[27] SALEM H. A. H.-VÄTH M.: An abstract Gronwall lemma and application to global existence results for functional differential and integral equations of fractional order. J. Integral Equations Appl. 16 (2004), 411-439. | MR

[28] SAMKO S.-KILBAS A.-MARICHEV O.: Fractional Integrals and Derivatives: Theory and Applications. Gordon and Breach Sci. PubL, New York, 1993. | MR | Zbl

[29] VÄTH M.: Ideal spaces. Lecture Notes in Math. 1664, Springer, Berlin-Heidelberg, 1997. | MR | Zbl

[30] SZEP A.: Existence theorem for weak solutions of differential equations in Banach spaces. Studia Sci. Math. Hungar. 6 (1971), 197-203. | MR